Linear Algebra — Full Problem Index (1/3)

{[x+2*y=1],[4*x+5*y=13])

[[7],[−3]]

Solve Using an Inverse Matrix x+2y=1 , 4x+5y=13

[[1/√(,17),(−4)/√(,17)]]*[[1/√(,17)],[(−4)/√(,17)]]

1

Multiply the Matrices

x+y=3

Domain:(−∞,∞)

Find the Domain x+y=3

x−y=3

Domain: *(−∞,∞)

Find the Domain x-y=3

y=−2*x+3

Domain: *(−∞,∞)

Find the Domain y=-2x+3

y=2*x+1

Domain:(−∞,∞)

Find the Domain y=2x+1

{[x=x2+9*x+3],[x=x+2])

[[x2+9*x+3],[x+2]]

Write as a Vector Equality x=x^2+9x+3 , x=x+2

y=2*x

Domain: *(−∞,∞)

Find the Domain y=2x

y=−3*x

Domain: *(−∞,∞)

Find the Domain y=-3x

y=3*x−2

Domain: *(−∞,∞)

Find the Domain y=3x-2

y=4*x

Domain: *(−∞,∞)

Find the Domain y=4x

3*x+2*y=6

Domain: *(−∞,∞)

Find the Domain 3x+2y=6

(I_5)

see full solution →

Find the 5x5 Identity Matrix 5

(I_6)

see full solution →

Find the 6x6 Identity Matrix 6

(I_4)

see full solution →

Find the 4x4 Identity Matrix 4

{[2*x+y=−2],[x+2*y=2])

(−2,2)

Solve Using an Inverse Matrix 2x+y=-2 , x+2y=2

{[4*x+4=y],[y=6*x])

(2,12)

Solve Using an Inverse Matrix 4x+4=y , y=6x

{[4*x+2=5*y−3],[y=3*x−1])

[[10/11],[19/11]]

Solve Using an Inverse Matrix 4x+2=5y-3 , y=3x-1

𝒫*({3,4})

{∅,{3},{4},{3,4}}

Find the Power Set (3,4)

√(3,216)

6

Evaluate cube root of 216

𝒫*({1,3})

{∅,{1},{3},{1,3}}

Find the Power Set (1,3)

3*x−2*y=12

Domain: *(−∞,∞)

Find the Domain 3x-2y=12

y=5*x+2

Domain: *(−∞,∞)

Find the Domain y=5x+2

y=2*x−3

Domain: *(−∞,∞)

Find the Domain y=2x-3

y=2*x−4

Domain: *(−∞,∞)

Find the Domain y=2x-4

y=2*x+5

Domain:(−∞,∞)

Find the Domain y=2x+5

y=1/(2*x)

Domain: *{[x∈ℝ,x≠0]}

Find the Domain y=1/2x

y=1/(2*x−3)

$\text{Domain: } {x

x \in \mathbb{R}, x \neq \frac{3}{2}}$

y=2/(3*x−2)

$\text{Domain: } {x

x \neq \frac{2}{3}}$

x=2*y

Domain: *(−∞,∞)

Find the Domain x=2y

x−2*y=2

Domain:(−∞,∞)

Find the Domain x-2y=2

x−2*y=6

Domain: *(−∞,∞)

Find the Domain x-2y=6

2*y+x

${(x, y)

x \in \mathbb{R}, y \in \mathbb{R}}$

2*x+y=0

Domain:(−∞,∞)

Find the Domain 2x+y=0

y=5*x+6

Domain: *(−∞,∞)

Find the Domain y=5x+6

y=x+3

Domain: *(−∞,∞)

Find the Domain y=x+3

{[y=4*x+3*x−2],[y=6])

(8/7,6)

Solve Using a Matrix by Elimination y=4x+3x-2 , y=6

B={[−10,2],[5,−2.5]}

False

[Determine if Linearly Dependent B={[[-10,2],[5,-2.5]]}](https://corca.app/doc/Ob1mxx0qmRcBzQv8mes45)

[[2,4],[6,−4]]+[[−3,−7],[20,10]]

[[−1,−3],[26,6]]

[Add [[2,4],[6,-4]]+[[-3,-7],[20,10]]](https://corca.app/doc/Wrz_iSo_tqLfCyI7orQTS)

B={[−1,2],[0,−2.5]}

The set *B* is linearly independent.

[Determine if Linearly Dependent B={[[-1,2],[0,-2.5]]}](https://corca.app/doc/_Tzpdj8fZlNQTes9Z-6-d)

[[0,0,1,1],[1,0,1,0],[0,0,0,1],[0,1,0,0]]*[[0,0,1,1],[1,0,1,0],[0,0,0,1],[0,1,0,0]]

see full solution →

Multiply the Matrices

y=5*x

Domain: *(−∞,∞)

Find the Domain y=5x

y=7*x

Domain: *(−∞,∞)

Find the Domain y=7x

y=−x−2

Domain: *(−∞,∞)

Find the Domain y=-x-2

y=x−2

(−∞,∞)

Find the Domain y=x-2

y=x−3

Domain: *(−∞,∞)

Find the Domain y=x-3

[[4,−3,1,0],[1,0,−2,0],[−2,1,1,0]]

see full solution →

[Find Reduced Row Echelon Form [[4,-3,1,0],[1,0,-2,0],[-2,1,1,0]]](https://corca.app/doc/2X54ct1dvE8URQUrBe0hC)

{[x+y+z=2],[4*x+5*y+z=12],[2*x=−4])

[[2],[12],[−4]]

Write as a Vector Equality x+y+z=2 , 4x+5y+z=12 , 2x=-4

det(0)

a2−6*a+8

[Find the Determinant [[0,-1,a],[3,-a,1],[1,-2,3]]](https://corca.app/doc/Vnbq43Z86YiA5gpqPsIRA)

y=−x+2

Domain: *(−∞,∞)

Find the Domain y=-x+2

det(2)

−46

[Find the Determinant [[2,5,0],[1,0,-3],[2,-1,2]]](https://corca.app/doc/F6s8hdYDg3XiGn2wJ73xA)

det(7)

131

[Find the Determinant [[7,5,0],[4,5,8],[0,-1,5]]](https://corca.app/doc/HS_fvBHmG64jaI6U-ql1l)

[[1,−3,0,−2],[3,−12,−2,−6],[−2,10,2,5],[−1,6,1,3]](−1)

see full solution →

Find the Inverse

[[1,2,3],[2,5,7],[3,7,9]]

see full solution →

[Find the Inverse [[1,2,3],[2,5,7],[3,7,9]]](https://corca.app/doc/YQ31WusRSTrNj0k1f70qD)

[[0,1,5,−4],[1,4,3,−2],[2,7,1,−2]]

see full solution →

[Find Reduced Row Echelon Form [[0,1,5,-4],[1,4,3,-2],[2,7,1,-2]]](https://corca.app/doc/JI6PKHVGY9Ohf99AlAuiA)

[[1,1,0],[1,0,1],[1,0,1],[2,1,0],[2,1,0]]

see full solution →

Find Reduced Row Echelon Form

[[1,2,3],[4,5,6],[7,8,9]]

see full solution →

[Find Reduced Row Echelon Form [[1,2,3],[4,5,6],[7,8,9]]](https://corca.app/doc/QguJJ3PKpsLciRA8S3fRj)

[[7,8]]

[[1,8/7]]

[Find Reduced Row Echelon Form [[7,8]]](https://corca.app/doc/5tn0Et-LWobhb_V1SoBTh)

2*x+y=1

Domain:(−∞,∞)

Find the Domain 2x+y=1

{[2*x+y=−2],[x+2*y=2])

[[−2],[2]]

Write as a Vector Equality 2x+y=-2 , x+2y=2

x−2*y=4

Domain:(−∞,∞)

Find the Domain x-2y=4

x−y=−1

−1* is *(−∞,∞)

Find the Domain x-y=-1

x+y=5

Domain: *(−∞,∞)

Find the Domain x+y=5

x=−3*y−8

Domain: *(−∞,∞)

Find the Domain x=-3y-8

x=−2*y−8

Domain: *(−∞,∞)

Find the Domain x=-2y-8

x+y=6

Domain: *(−∞,∞)

Find the Domain x+y=6

x+y=4

Domain: *(−∞,∞)

Find the Domain x+y=4

x+2*y=4

Domain: *(−∞,∞)

Find the Domain x+2y=4

x+y

see full solution →

Find the Domain x+y

y=7*x+9

Domain: *(−∞,∞)

Find the Domain y=7x+9

y=1/(2*x−5)

Domain: *{[x∈ℝ,x≠5/2]}

Find the Domain y=1/2x-5

y=1/(2*x+2)

$\text{Domain: } {x

x \in \mathbb{R}, x \neq -1}$

y=1/(2*x+3)

see full solution →

Find the Domain y=1/2x+3

x−y=−3

Domain:(−∞,∞)

Find the Domain x-y=-3

x−y=4

Domain: *(−∞,∞)

Find the Domain x-y=4

y=−2*x

Domain: *(−∞,∞)

Find the Domain y=-2x

y=−2*x+1

Domain: *(−∞,∞)

Find the Domain y=-2x+1

y=2(x+9)

Domain: *(−∞,∞)

Find the Domain y=2^(x+9)

y=10−x2

Domain: *(−∞,∞)

Find the Domain y=10-x^2

y=2*x−6

Domain: *(−∞,∞)

Find the Domain y=2x-6

y=−2*x−3

Domain: *(−∞,∞)

Find the Domain y=-2x-3

y=3*x−8

Domain: *(−∞,∞)

Find the Domain y=3x-8

y=3*x

Domain: *(−∞,∞)

Find the Domain y=3x

y=−3*x+1

Domain: *(−∞,∞)

Find the Domain y=-3x+1

y=4*x+3

Domain: *(−∞,∞)

Find the Domain y=4x+3

y=3*x−4

Domain: *(−∞,∞)

Find the Domain y=3x-4

y=4*x−2

Domain: *(−∞,∞)

Find the Domain y=4x-2

y=−6*x

Domain: *(−∞,∞)

Find the Domain y=-6x

y=x−4

Domain:(−∞,∞)

Find the Domain y=x-4

7√(4,567*y4)

Domain: *(−∞,∞)

Find the Domain 7 fourth root of 567y^4

c=5/9*(ƒ−32)

Domain: *(−∞,∞)

Find the Domain c=5/9*(f-32)

ƒ=9/5*c+32

Domain: *(−∞,∞)

Find the Domain f=9/5c+32

√(,4)

2

Evaluate square root of 4

[[−6,7],[2,6],[−4,1]]

[[1,0],[0,1],[0,0]]

[Find Reduced Row Echelon Form [[-6,7],[2,6],[-4,1]]](https://corca.app/doc/s8fm6xuC9FvEzfOlDDghV)

[[2,1],[3,2]]

2+√(,3),2−√(,3)

[Find the Eigenvalues [[2,1],[3,2]]](https://corca.app/doc/aa8jvT84eQOjkvEbMJ5hO)

det([[4,0,1],[2,3,2],[49,0,4]]−λ*I)=0

3, 11, -3$

[Find the Eigenvalues [[4,0,1],[2,3,2],[49,0,4]]](https://corca.app/doc/jkSitT5yVuvLz0gKzwXv1)

𝒫*({2,3,4,5})

see full solution →

Find the Power Set A=(2,3,4,5)

(

(2, 1)

)

{[−3*x−4*y=2],[8*y=−6*x−4])

0

Solve Using an Inverse Matrix -3x-4y=2 , 8y=-6x-4

{[2*x−5*y=4],[3*x−2*y=−5])

[[−3],[−2]]

Solve Using an Inverse Matrix 2x-5y=4 , 3x-2y=-5

{[x+3*y=−6],[3*x+2*y=3])

[[3],[−3]]

Solve Using an Inverse Matrix x+3y=-6 , 3x+2y=3

{[x+2*y=1],[5*y=15])

[[−5],[3]]

Solve Using an Inverse Matrix x+2y=1 , 5y=15

{[2*x−6*y=7],[5*x+2*y=10])

see full solution →

Solve Using an Inverse Matrix 2x-6y=7 , 5x+2y=10

2⋅(I_2)

([2,0],[0,2])

Find the Result of 2 Times the 2x2 Identity Matrix 2

3⋅(I_3)

see full solution →

Find the Result of 3 Times the 3x3 Identity Matrix 3

(I_7)

see full solution →

Find the 7x7 Identity Matrix 7

(I_9)

see full solution →

Find the 9x9 Identity Matrix 9

5⋅(I_5)

see full solution →

Find the Result of 5 Times the 5x5 Identity Matrix 5

{[x−z+3*y=4],[z=3*y],[y−x=5*z])

see full solution →

Solve Using an Inverse Matrix x-z+3y=4 , z=3y , y-x=5z

{[x−y=3],[4*x+y=17])

[[4],[1]]

Solve Using an Inverse Matrix x-y=3 , 4x+y=17

{[x−y=7],[x−y=5])

No solution

Solve Using an Inverse Matrix x-y=7 , x-y=5

{[x−2*y=3],[−2*x+4*y=6])

No solution

Solve Using an Inverse Matrix x-2y=3 , -2x+4y=6

{[x+y=48],[x=8*y])

$\frac{128}{3} \\ y = \frac{16}{3} \end{cases}$

Solve Using an Inverse Matrix x+y=48 , x=8y

{[x+y=6],[2*x−3*y=2])

[[4],[2]]

Solve Using an Inverse Matrix x+y=6 , 2x-3y=2

{[x−3*y=−6],[5*x+3*y=42])

(6,4)

Solve Using an Inverse Matrix x-3y=-6 , 5x+3y=42

{[x−y=−2],[7*x+3*y=−66])

[[−7.2],[−5.2]]

Solve Using an Inverse Matrix x-y=-2 , 7x+3y=-66

{[y=3*x+1],[3*y−4*x=13])

(2,7)

Solve Using an Inverse Matrix y=3x+1 , 3y-4x=13

{[x+y=6],[x−y=2])

(4,2)

Solve Using an Inverse Matrix x+y=6 , x-y=2

{[x+y=19],[x−4*y=−1])

[[15],[4]]

Solve Using an Inverse Matrix x+y=19 , x-4y=-1

{[x+y+z=8],[2*x−y−z=10],[x−2*y−3*z=22])

[[6],[22],[−20]]

Solve Using an Inverse Matrix x+y+z=8 , 2x-y-z=10 , x-2y-3z=22

{[x−3*z=−2],[2*x+2*y+z=4],[3*x+y−2*z=5])

[[4],[−3],[2]]

Solve Using an Inverse Matrix x-3z=-2 , 2x+2y+z=4 , 3x+y-2z=5

[[0,1,0],[0,0,1],[125*x3,−75*x2,15*x]]

3×3

[Find the Dimensions [[0,1,0],[0,0,1],[125x^3,-75x^2,15x]]](https://corca.app/doc/xCkW1-g3Wgdphu0K4wdg8)

{[y=3.2+x],[7.1−x=7.2*y])

(−797/410,103/82)

Solve Using an Inverse Matrix y=3.2+x , 7.1-x=7.2y

(I_2)

([1,0],[0,1])

Find the 2x2 Identity Matrix 2

−3*X+[[7,0,−1],[2,−3,4]]=[[10,0,8],[−19,−18,10]]

see full solution →

Solve the Matrix Equation

4⋅(I_4)

see full solution →

Find the Result of 4 Times the 4x4 Identity Matrix 4

[[4,−10,29],[1,−2,5],[−3,7,−19]]

see full solution →

[Find the Inverse [[4,-10,29],[1,-2,5],[-3,7,-19]]](https://corca.app/doc/QoQJAOZVWUmSsTyv01h9t)

[[2*x+3*y],[3*x−y]]=[[7],[16]]

see full solution →

[Solve the Matrix Equation [[2x+3y],[3x-y]]=[[7],[16]]](https://corca.app/doc/TeNp2sgS2PhDrbIIb8iLP)

[[1,0,−5,0,−14],[0,1,2,0,−7],[0,0,0,1,7],[0,0,0,0,8]]

Pivot Positions: *(1,1),(2,2),(3,4),(4,5)

Find Pivot Positions and Pivot Columns

{[3*x+y=10],[3*x−2*y=16])

[[4],[−2]]

Solve Using an Inverse Matrix 3x+y=10 , 3x-2y=16

{[2*y=−7*x+3],[−7*x−6*y=5])

[[1],[−2]]

Solve Using an Inverse Matrix 2y=-7x+3 , -7x-6y=5

{[−4*x+9*y=41],[5*x−4*y=−44])

[[−8],[1]]

Solve Using an Inverse Matrix -4x+9y=41 , 5x-4y=-44

{[4*x−5*y=22],[x+2*y=−1])

(3,−2)

Solve Using an Inverse Matrix 4x-5y=22 , x+2y=-1

{[3*x+y=−9],[6*x+2*y=6])

No solution

Solve Using an Inverse Matrix 3x+y=-9 , 6x+2y=6

{[3*y−5=x],[x+y=115])

$x \\ x + y = 115 \end{cases} \Rightarrow (x, y) = (85, 30)$

Solve Using an Inverse Matrix 3y-5=x , x+y=115

{[2*x+y=8],[4*x+2*y=24])

No solution (The system is inconsistent)

Solve Using an Inverse Matrix 2x+y=8 , 4x+2y=24

{[2*x+y=8],[x+2*y=1])

[[5],[−2]]

Solve Using an Inverse Matrix 2x+y=8 , x+2y=1

{[3*x−y−z=3],[−2*x+3*y+z=3],[4*x−2*y−2*z=2])

[[2],[2],[1]]

Solve Using an Inverse Matrix 3x-y-z=3 , -2x+3y+z=3 , 4x-2y-2z=2

{[3*y=11−2*x],[3*x=y−11])

(−2,5)

Solve Using an Inverse Matrix 3y=11-2x , 3x=y-11

{[4*r+7*s=23],[r−2*s=17])

[[11],[−3]]

Solve Using an Inverse Matrix 4r+7s=23 , r-2s=17

{[7*x−5*y=12],[2*x+3*y=9])

[[81/31],[39/31]]

Solve Using an Inverse Matrix 7x-5y=12 , 2x+3y=9

{[2*x+4*y=6],[4*x+8*y=0])

No Solution

Solve Using an Inverse Matrix (2x+4y)=6 , (4x+8y)=0

{[y=x−5*x+6],[y=x−2])

(8/5,−2/5)

Solve Using an Inverse Matrix y=x-5x+6 , y=x-2

{[x+4*y=13],[2*x−y=−1])

[[1],[3]]

Solve Using an Inverse Matrix x+4y=13 , 2x-y=-1

{[4*x+3*y=−2],[x−y=−4])

[[−2],[2]]

Solve Using an Inverse Matrix 4x+3y=-2 , x-y=-4

{[x+2*y−z=4],[2*x+y+z=−2],[x+2*y+z=2])

[[−5/3],[7/3],[−1]]

Solve Using an Inverse Matrix x+2y-z=4 , 2x+y+z=-2 , x+2y+z=2

{[x+3*y=1],[x−y=6])

[[19/4],[−5/4]]

Solve Using an Inverse Matrix x+3y=1 , x-y=6

{[x+3*y=10],[3*x+9*y=16])

No solution

Solve Using an Inverse Matrix x+3y=10 , 3x+9y=16

{[x+y+z=12],[2*x−3*y+2*z=4],[x+z=2*y])

(8−t,4,t)

Solve Using an Inverse Matrix x+y+z=12 , 2x-3y+2z=4 , x+z=2y

{[−7*x−2*y=−13],[x−2*y=11])

(3,−4)

Solve Using an Inverse Matrix -7x-2y=-13 , x-2y=11

{[6*x−y+3*z=−13],[x+3*y−z=−4],[3*x+3*y−4*z=3])

[[−1],[−2],[−3]]

Solve Using an Inverse Matrix 6x-y+3z=-13 , x+3y-z=-4 , 3x+3y-4z=3

{[8*x+6*y=−4],[9*x−6*y=−81])

[[−5],[6]]

Solve Using an Inverse Matrix 8x+6y=-4 , 9x-6y=-81

{[5*x+4*y=−2],[3*x−3*y=2])

(2/27,−16/27)

Solve Using an Inverse Matrix 5x+4y=-2 , 3x-3y=2

{[−5*x+y=7],[x+y=1])

[[−1],[2]]

Solve Using an Inverse Matrix -5x+y=7 , x+y=1

{[−5*x+y=−8],[y=−4*x+1])

[[1],[−3]]

Solve Using an Inverse Matrix -5x+y=-8 , y=-4x+1

{[−5*x−9*y=11],[4*x+5*y=0])

[[5],[−4]]

Solve Using an Inverse Matrix -5x-9Y=11 , 4x+5y=0

{[x=2*y−5],[2*x−4*y=−10])

The system has infinitely many solutions.

Solve Using an Inverse Matrix x=2y-5 , 2x-4y=-10

{[2*x+4*y=25],[x+5*y=2])

[[39/2],[−7/2]]

Solve Using an Inverse Matrix 2x+4y=25 , x+5y=2

{[−2*x+2*y+3*z=1],[x−y=3],[y+4*z=−2])

see full solution →

Solve Using an Inverse Matrix -2x+2y+3z=1 , x-y=3 , y+4z=-2

{[2*x+y=4],[−6*x−3*y=−12])

Infinitely many solutions of the form *(x,4−2*x)

Solve Using an Inverse Matrix 2x+y=4 , -6x-3y=-12

{[y=6−2*x],[7*x−y=3])

(1,4)

Solve Using an Inverse Matrix y=6-2x , 7x-y=3

{[15*x+11*y=32],[−9*x+7*y=8])

[[2/3],[2]]

Solve Using an Inverse Matrix 15x+11y=32 , 7y-9x=8

{[x=−3*y+39],[3*x+4*y=67])

[[9],[10]]

Solve Using an Inverse Matrix x=-3y+39 , 3x+4y=67

{[20=8*y+11*x],[11*x+8*y=79])

No solution

Solve Using an Inverse Matrix 20=8y+11x , 11x+8y=79

{[2*b+c+z=11],[3*b+4*c+z=19],[3*b+6*c+5*z=43])

[[2],[2],[5]]

Solve Using an Inverse Matrix 2b+c+z=11 , 3b+4c+z=19 , 3b+6c+5z=43

{[−(y−4)=x+9],[x−8/3*y=0])

[[−40/11],[−15/11]]

Solve Using an Inverse Matrix -(y-4)=x+9 , x-8/3y=0

{[2*x+3*y=−16],[5*x−10*y=20])

[[−20/7],[−24/7]]

Solve Using an Inverse Matrix 2x+3y=-16 , 5x-10y=20

{[2*x+3*y=8],[3*x−y=1])

[[1],[2]]

Solve Using an Inverse Matrix 2x+3y=8 , 3x-y=1

{[2*x+5*y=1],[4*x+20*y=6])

[[−0.5],[0.4]]

Solve Using an Inverse Matrix 2x+5y=1 , 4x+20y=6

{[2*x+5*y=1],[6*x+15*y=3])

The system has infinitely many solutions.

Solve Using an Inverse Matrix 2x+5y=1 , 6x+15y=3

{[−2*x=27−5*y],[4*y=20+2*x])

[[4],[7]]

Solve Using an Inverse Matrix -2x=27-5y , 4y=20+2x

{[2*x−y=9],[6*x−3*y=9])

No solution

Solve Using an Inverse Matrix 2x-y=9 , 6x-3y=9

{[3*x+5*y=11],[x+3*y=13])

[[−8],[7]]

Solve Using an Inverse Matrix 3x+5y=11 , x+3y=13

adj*[[1,0,0],[0,2,6],[0,−4,−12]]

see full solution →

[Find the Adjoint [[1,0,0],[0,2,6],[0,-4,-12]]](https://corca.app/doc/mlwryatzgxOOBtCWlLSxL)

(

(-3, 4)

)

{[26*a+8*b=28],[8*a+3*b=9])

[[6/7],[5/7]]

Solve Using an Inverse Matrix 26a+8b=28 , 8a+3b=9

{[2*x+2*y=2],[3*x−y=1])

[[1/2],[1/2]]

Solve Using an Inverse Matrix 2x+2y=2 , 3x-y=1

{[2*x+5*y=−4],[3*x−y=11])

(3,−2)

Solve Using an Inverse Matrix 2x+5y=-4 , 3x-y=11

{[x+y=−2],[x−2*y=10])

[[2],[−4]]

Solve Using an Inverse Matrix x+y=-2 , x-2y=10

y−9=3/(5*x)

(−∞,0)∪(0,∞)

Find the Domain y-9=3/5x

{[5*y=x−1],[x−y=1])

(1,0)

Solve Using an Inverse Matrix 5y=x-1 , x-y=1

(

(2,0)

)

B={5,4,3,2,1,0}

6

Find the Cardinality B=(5,4,3,2,1,0)

Q={5,6,7,8}

4

Find the Cardinality Q=(5,6,7,8)

(

(0, 5)

)

(

(-2, 3)

)

(

(-3, 7)

)

(

(0,0)

)

𝒫*({3,6,8})

see full solution →

Find the Power Set Y=(3,6,8)

𝒫*({1,2})

{∅,{1},{2},{1,2}}

Find the Power Set {1,2}

𝒫*({1,2,3,4})

see full solution →

Find the Power Set A=(1,2,3,4)

𝒫*({1,2,3,4,5,6})

see full solution →

Find the Power Set A=(1,2,3,4,5,6)

A={4,6,8,9}

4

Find the Cardinality A=(4,6,8,9)

y=−2*x2

Domain: *(−∞,∞)

Find the Domain y=-2x^2

adj*[[3,4,−1],[2,−2,3],[1,−1,x]]

see full solution →

[Find the Adjoint [[3,4,-1],[2,-2,3],[1,-1,x]]](https://corca.app/doc/ioDVCef8RR0_aCYXC6FBM)

(2√(,3)+√(,6))/(4√(,3)−√(,6))

(5+3√(,2))/7

Evaluate

[[1,0,−2,2],[−3,−1,0,−3],[−3,−2,2,3],[−3,1,0,0]]

see full solution →

Find the Cofactor Matrix

[[5,2],[4,3]]

[[3,−4],[−2,5]]

[Find the Cofactor Matrix [[5,2],[4,3]]](https://corca.app/doc/MtEnxvVf-aRbI_yXIs6EA)

[[1,−1,−2],[1,3,2],[1,−1,2]]

2, 2 + 2i, 2 - 2i$

[Find the Eigenvalues [[1,-1,-2],[1,3,2],[1,-1,2]]](https://corca.app/doc/QBfG0UHYL7OKRJmh8wZYi)

[[−6,5]]

[[1,−5/6]]

[Find Reduced Row Echelon Form [[-6,5]]](https://corca.app/doc/GqpExAbyaL3NL0dxZSmLr)

[[7,6]]

[[1,6/7]]

[Find Reduced Row Echelon Form [[7,6]]](https://corca.app/doc/64A_ouCtxx-JRZCjI_rY_)

[[2,1,1],[1,2,1],[1,1,2]]

1, 1, 4$

[Find the Eigenvalues [[2,1,1],[1,2,1],[1,1,2]]](https://corca.app/doc/4cX0Ig8tzkK7yWvit7EoC)

A=[[1,3,0,0],[2,2,0,0],[0,0,1,3],[0,0,2,2]]

(λ2−3*λ−4)2=0

Find the Characteristic Equation

A=[[4,1,7,2],[0,3,−1,5],[0,0,8,3],[0,0,0,4]]

(λ−4)2*(λ−3)*(λ−8)=0

Find the Characteristic Equation

A=[[6,−3],[−2,1]]

see full solution →

[Find the Eigenvectors/Eigenspace A=[[6,-3],[-2,1]]](https://corca.app/doc/3DFZEYnH7AwEV0ljiVeJQ)

det([[2,4,6],[4,5,6],[3,1,−2]]−λ*I)=0

−λ3+5*λ2+44*λ+6=0

[Find the Characteristic Equation [[2,4,6],[4,5,6],[3,1,-2]]](https://corca.app/doc/oO2w-YP-72dd32XpkvD32)

A=[[1,0,0],[1,2,0],[−3,5,2]]

see full solution →

[Find the Eigenvectors/Eigenspace A=[[1,0,0],[1,2,0],[-3,5,2]]](https://corca.app/doc/QDbyVE4A503GMV6pT47fs)

[[1,−1,0],[−1,2,−1],[0,−1,1]]

see full solution →

[Find the Eigenvectors/Eigenspace [[1,-1,0],[-1,2,-1],[0,-1,1]]](https://corca.app/doc/WCNzR_ZuOUkUWSu2Rsntq)

[[2,1],[3,4]]

5, 1$

[Find the Eigenvalues [[2,1],[3,4]]](https://corca.app/doc/sw6Kq6KIjynmFPgE_BPT3)

[[−4,0,1],[3,−6,3],[1,0,−4]]

−6,−5,−3

[Find the Eigenvalues [[-4,0,1],[3,-6,3],[1,0,-4]]](https://corca.app/doc/x3xwditYPk8B-bqL6hO59)

det([[6,8,9],[x,8,6],[5,6,5]]−λ*I)=0

0

[Find the Eigenvalues [[6,8,9],[x,8,6],[5,6,5]]](https://corca.app/doc/5CVwSyRFZaRVU9-68pBBb)

[[6,−8,10],[−3/4,1,−5/4]]

see full solution →

[Find Reduced Row Echelon Form [[6,-8,10],[-3/4,1,-5/4]]](https://corca.app/doc/hwDajgVKf_sVTpsFTZFMQ)

[[2,3],[1,1]](−1)

[[−1,3],[1,−2]]

[Find the Inverse [[2,3],[1,1]]](https://corca.app/doc/opiHWo20-5NSKyyMn8aHn)

[[1,−9,16],[0,0,0]]

[[1,−9,16],[0,0,0]]

[Find Reduced Row Echelon Form [[1,-9,16],[0,0,0]]](https://corca.app/doc/u93DDt8b5e6YJdXMKpj0B)

[[3,−2,7,63],[2,1,−21,28],[1,4,−49,−7]]

see full solution →

[Find Reduced Row Echelon Form [[3,-2,7,63],[2,1,-21,28],[1,4,-49,-7]]](https://corca.app/doc/-03176w7ivUJb2W6OGauv)

[[7,2,1,0],[3,7,0,1]]

see full solution →

[Find Reduced Row Echelon Form [[7,2,1,0],[3,7,0,1]]](https://corca.app/doc/lxYVg4MQ4t4DF9GgnmEgS)

[[7,2,2],[2,2,7]]

see full solution →

[Find Reduced Row Echelon Form [[7,2,2],[2,2,7]]](https://corca.app/doc/Tlh_d53CRq8nPkbT8ABM4)

[[2,−1,1],[3,1,−2],[−1,2,5]]

see full solution →

[Transpose [[2,-1,1],[3,1,-2],[-1,2,5]]](https://corca.app/doc/FMaKKRkULIbL8faxA1BYf)

[[3,1,0],[−1,0,4],[2,2,1]]

see full solution →

[Transpose [[3,1,0],[-1,0,4],[2,2,1]]](https://corca.app/doc/yo49oxWGJ2NHPzjjJPtVU)

[[0,1],[−1,0]]

i,−i

[Find the Eigenvalues [[0,1],[-1,0]]](https://corca.app/doc/lJTx1c0L8BV3zAXLNe-Ku)

[[1,1],[−1,1]]

1 + i, 1 - i$

[Find the Eigenvalues [[1,1],[-1,1]]](https://corca.app/doc/97zV_EPgel15xKa3rCmqF)

[[a,b,1,0],[c,d,0,1]]

see full solution →

[Find Reduced Row Echelon Form [[a,b,1,0],[c,d,0,1]]](https://corca.app/doc/7_Zh1lsEhI5PV2b6Czm40)

[[1,2],[3,4]]T

[[1,3],[2,4]]

[Transpose [[1,2],[3,4]]](https://corca.app/doc/_cuVKLCX5JnuMu_sH7vpl)

[[5,2],[3,6]]T

[[5,3],[2,6]]

[Transpose [[5,2],[3,6]]](https://corca.app/doc/mzhun8ho268ARoTZWdJFh)

A=[[1,2,1],[0,3,1],[0,5,−1]]

see full solution →

[Find the Eigenvectors/Eigenspace [[1,2,1],[0,3,1],[0,5,-1]]](https://corca.app/doc/pnlobkahGL6trSKec8nZM)

[[1,0,1],[0,−1,0],[2,1,−1]]

see full solution →

[Find the Eigenvectors/Eigenspace [[1,0,1],[0,-1,0],[2,1,-1]]](https://corca.app/doc/HadZAMgQ6Yq2gVdCDYD-1)

[[1,3],[4,2]]

see full solution →

[Find the Eigenvectors/Eigenspace [[1,3],[4,2]]](https://corca.app/doc/MyW3nB7FCrQCDTF_9K6vw)

[[1.3,0.4],[−0.2,1.9]]

see full solution →

[Find the Eigenvectors/Eigenspace [[1.3,0.4],[-0.2,1.9]]](https://corca.app/doc/Fyzfm_JdGoER6bA5gCBlM)

[[2,1,1],[1,2,1],[1,1,2]]

see full solution →

[Find the Eigenvectors/Eigenspace [[2,1,1],[1,2,1],[1,1,2]]](https://corca.app/doc/DhLoQf3T5O73-DXcLW-tE)

[[−2,−1,−1],[−2,−3,−2],[2,2,1]]

see full solution →

[Find the Eigenvectors/Eigenspace [[-2,-1,-1],[-2,-3,-2],[2,2,1]]](https://corca.app/doc/UIggL9j1Up97M4_k-WcaU)

A=[[3,0,−1],[2,3,1],[−3,4,5]]

see full solution →

[Find the Eigenvectors/Eigenspace [[3,0,-1],[2,3,1],[-3,4,5]]](https://corca.app/doc/qx7kGhnTLXpu4-A1SmV-o)

A=[[3,2],[4,6]]

λ2−9*λ+10=0

[Find the Characteristic Equation [[3,2],[4,6]]](https://corca.app/doc/N1G4uZ8cHJjOpWvDj_e3k)

[[4,−4],[−2,2]]

see full solution →

[Find the Eigenvectors/Eigenspace [[4,-4],[-2,2]]](https://corca.app/doc/BZOLNtHM6skhMYh1vYNTK)

[[5,0],[2,3]]

see full solution →

[Find the Eigenvectors/Eigenspace [[5,0],[2,3]]](https://corca.app/doc/a0zdsK6Dw7Vk2aBhP2u97)

[[5,3],[3,5]]

see full solution →

[Find the Eigenvectors/Eigenspace [[5,3],[3,5]]](https://corca.app/doc/AHDr6_FqNS2tKRQSN-ST3)

Null Space*[[0,4,−3,−1],[4,4,−2,−2],[−1,−1,1,−1],[0,2,1,3]]

see full solution →

Find the Null Space

[[8,6],[−3,2]]

see full solution →

[Find the Eigenvectors/Eigenspace [[8,6],[-3,2]]](https://corca.app/doc/ymhWiev-0R-T9cBzKDtMU)

Null Space*[[2,1],[1,3]]

{[0],[0]}

[Find the Null Space [[2,1],[1,3]]](https://corca.app/doc/zv0b-h8TqTJ4NPxCezofM)

Null Space*[[1,4,0,3,0],[0,0,1,−3,0],[0,0,0,0,−1]]

see full solution →

[Find the Null Space [[1,4,0,3,0],[0,0,1,-3,0],[0,0,0,0,-1]]](https://corca.app/doc/S78YtsUSGfnGIG6ev5sxl)

null*[[2,4,6,4],[2,5,7,6],[2,3,5,2]]

see full solution →

[Find the Null Space s=[[2,4,6,4],[2,5,7,6],[2,3,5,2]]](https://corca.app/doc/j1qkGbIq-OuZFjrvHUTte)

Null Space*[[7,6,2],[6,3,1],[5,5,6]]

{[0],[0],[0]}

[Find the Null Space [[7,6,2],[6,3,1],[5,5,6]]](https://corca.app/doc/fMDBB72gSiLc77vy6-dN5)

|[−3,0,−6],[−2,3,4]|F

√(,74)

[Find the Norm [[-3,0,-6],[-2,3,4]]](https://corca.app/doc/CewVZGvc3u1CRdXfZkIsV)

rank(1)

3

Find the Rank

[[1,0],[6,−1]]

see full solution →

[Find the Eigenvectors/Eigenspace [[1,0],[6,-1]]](https://corca.app/doc/FI0WVCd-TS36Y3mwSc_5H)

{[2*x+2*y=−16],[y=−x−8])

Infinitely many solutions of the form *(x,−x−8)

Solve Using an Inverse Matrix 2x+2y=-16 , y=-x-8

√(,4+76−4)

2√(,19)

Evaluate square root of 4+76-4

(−3−5*i)−(4+2*i)

7√(,2)*(cos((5*π)/4)+i*sin((5*π)/4))

Convert to Trigonometric Form (-3-5i)-(4+2i)

2+7*i+(−6+i)

4√(,5)*(cos(2.034)+i*sin(2.034))

Convert to Trigonometric Form 2+7i+(-6+i)

(11+√(,15))*(11−√(,15))

106

Evaluate

√(,(−7)2+(5)2)

√(,74)

Evaluate square root of (-7)^2+(5)^2

Nullity*[[1,2,2,3],[−1,−3,3,2],[2,−3,4,6]]

1

[Find the Nullity [[1,2,2,3],[-1,-3,3,2],[2,-3,4,6]]](https://corca.app/doc/qtpovl5beNS8u5KEk2K39)

Nullity*[[1,0,1,0,6],[1,1,2,2,0],[0,0,1,0,0],[0,0,0,0,0]]

2

Find the Nullity

null*[[2],[1],[4]]

{0}

[Find the Null Space [[2],[1],[4]]](https://corca.app/doc/CsPw83ANV-n99sa7ktsmn)

Nullity*[[1,−1,3],[6,7,−3],[9,4,6]]

1

[Find the Nullity [[1,-1,3],[6,7,-3],[9,4,6]]](https://corca.app/doc/r760qNB9ddYSLavsYtcxb)

[[1,5],[4,8]]*[[x],[y]]=[[−20],[−44]]

see full solution →

[Determine if Linear [[1,5],[4,8]]*[[x],[y]]=[[-20],[-44]]](https://corca.app/doc/KbCsjOTsb7NYOKKr3ZkOc)

X−[[0,1,5,−6],[5,8,7,−1]]=[[1,2,3,6],[−8,−4,−2,−3]]

see full solution →

Determine if Linear

A=[[1],[5],[6]],x=[[1,−2,8]]

see full solution →

[Project Using the Transformation A=[[1],[5],[6]] , x=[[1,-2,8]]](https://corca.app/doc/_JCYEEihYKaG49cu7yijQ)

[[1,0,1],[−1,21,0]]+[[2,2,−2],[−3,4,3]]

[[3,2,−1],[−4,25,3]]

Simplify the Matrix

Ker(S)* where *S*([a],[b],[c])=([a−b−c],[a−b−c],[a−b+c])

see full solution →

Find the Kernel

T*[[x],[y]]=[[y],[x]]

[[y],[x]]* is linear

[Determine if Linear [[x],[y]]=[[y],[x]]](https://corca.app/doc/FRgu0sddz2wR7mmjiwn4q)

4√(3,24)

8√(3,3)

Evaluate 4 cube root of 24

{3,4,6,1}∩{0,9,8,7,1}

{1}

Find the Intersection of the Sets A=(3,4,6,1) , B=(0,9,8,7,1)

det([[0.30,0.20,0.30],[0.40,0.30,0.30],[0.30,0.30,0.20]]−[[1,0,0],[0,1,0],[0,0,1]])

−0.148

Find the Determinant of the Resulting Matrix

−12√(,1+5)

−12√(,6)

Evaluate -12 square root of 1+5

𝒫*({0,2})

{∅,{0},{2},{0,2}}

Find the Power Set (0,2)

𝒫*({0,5})

{∅,{0},{5},{0,5}}

Find the Power Set (0,5)

𝒫*({1,4})

{∅,{1},{4},{1,4}}

Find the Power Set (1,4)

[[8,93,0.01],[44,575,5],[1,0.1,0.1]]*[[8,24,5],[8,9,6],[0.1,1,2]]

see full solution →

Find the Inverse of the Resulting Matrix

𝒫*({−1,3})

{∅,{−1},{3},{−1,3}}

Find the Power Set (-1,3)

𝒫*({−2,3})

{∅,{−2},{3},{−2,3}}

Find the Power Set (-2,3)

𝒫*({0,9})

{∅,{0},{9},{0,9}}

Find the Power Set (0,9)

𝒫*({3,−4})

{∅,{3},{−4},{3,−4}}

Find the Power Set (3,-4)

𝒫*({2,−3})

{∅,{2},{−3},{2,−3}}

Find the Power Set (2,-3)

Power Set*({4,2})

{∅,{4},{2},{4,2}}

Find the Power Set (4,2)

𝒫*({3,2})

{∅,{3},{2},{3,2}}

Find the Power Set (3,2)

[[4,5,9,−2],[6,5,1,12],[3,4,8,−3]]

3×4

[Find the Dimensions [[4,5,9,-2],[6,5,1,12],[3,4,8,-3]]](https://corca.app/doc/EpclpPbPINjJ6g70bqkzR)

[[1,2],[5,5],[10,3],[4,6],[7,0]]

5×2

[Find the Dimensions [[1,2],[5,5],[10,3],[4,6],[7,0]]](https://corca.app/doc/vtG5cFexdjgLsPnaJWOhH)

[[−2,3,1,4]]

1×4

[Find the Dimensions [[-2,3,1,4]]](https://corca.app/doc/H1bluiV5iD3Tz7nPb26N0)

[[1,2,3,4],[40,−11,−55.7,−95.99]]

2×4

[Find the Dimensions [[1,2,3,4],[40,-11,-55.7,-95.99]]](https://corca.app/doc/LBABuPTD3y2--86nHzcpi)

[[1,2]]

1×2

[Find the Dimensions [[1,2]]](https://corca.app/doc/s3HY0j-mT9q9bWj3ZbDfR)

[[4,2],[6,7]]

2×2

[Find the Dimensions [[4,2],[6,7]]](https://corca.app/doc/F9O3uXvfJVZaKh0ET2VGe)

ƒ(x)=−x4+4*x2−x−5

Domain: *(−∞,∞)

Find the Domain f(x)=-x^4+4x^2-x-5

ƒ(x)=1.5*x−3

Domain: *(−∞,∞)

Find the Domain f(x)=1.5x-3

ƒ(x)=2*x−3

Domain:(−∞,∞)

Find the Domain f(x)=2x-3

ƒ(x)=4*x2+1/x

Domain: *(−∞,0)∪(0,∞)

Find the Domain f(x)=4x^2+1/x

ƒ(x)=(x2−7*x+10)/(x2−25)

$\text{Domain}: {x

x \in \mathbb{R}, x \neq 5, x \neq -5}$

ƒ(x)=(x−1)*(x+4)*(x−5)

Domain: *(−∞,∞)

Find the Domain f(x)=(x-1)(x+4)(x-5)

( f(x) = \frac{x^3 - x^2 + 1}{

x

} )

ƒ(x)=1/(3*x)+4

Domain: *{[x∈ℝ,x≠0]}

Find the Domain f(x)=1/3(x)+4

ƒ(x)=5/3*(4/5)x

Domain: *(−∞,∞)

Find the Domain f(x)=5/3*(4/5)^x

d=v*(x2−x+(y2−y))⋅22

{(x,y)∈ℝ2:x2−x+y2−y≥0}

Find the Domain d=v(x^2-x+(y^2-y))*22

ƒ(x)=−x2

Domain: *(−∞,∞)

Find the Domain f(x)=-x^2

9*x+8*y=29

(−∞,∞)

Find the Domain 9x+8y=29

6*x−3*y=12

Domain: *(−∞,∞)

Find the Domain 6x-3y=12

c*(A)t=1/C*at

(−∞,∞)

Find the Domain c(A)^t=(1/C)a^t

8*x−3*y+12=0

Domain: *(−∞,∞)

Find the Domain 8x-3y+12=0

9*x3+2*x−8*x3−3*x

Domain: *(−∞,∞)

Find the Domain 9x^3+2x-8x^3-3x

9*x−5−2*x=16

Domain: *(−∞,∞)

Find the Domain 9x-5-2x=16

7*x+8*y=51.30

Domain: *(−∞,∞)

Find the Domain 7x+8y=51.30

7*x−4*y=−3

Domain: *(−∞,∞)

Find the Domain 7x-4y=-3

8+2(x+1)=2(2*x)

(−∞,∞)

Find the Domain 8+2^(x+1)=2^(2x)

6*x−5*y=10

Domain: *(−∞,∞)

Find the Domain 6x-5y=10

6*x+3*y=18

Domain: *(−∞,∞)

Find the Domain 6x+3y=18

6*x2+5*x−6

Domain: *(−∞,∞)

Find the Domain 6x^2+5x-6

−6*x=12

Domain: *(−∞,∞)

Find the Domain -6x=12

−7*y2+z*y−x=0

{[(x,z)∈ℝ2,x≤(z2)/28]}

Find the Domain -7y^2+zy-x=0

2*x−y=6

Domain: *(−∞,∞)

Find the Domain 2x-y=6

3*x+y=0

Domain: *(−∞,∞)

Find the Domain 3x+y=0

3*x+y=10

Domain: *(−∞,∞)

Find the Domain 3x+y=10

3*x−2*y=−16

Domain: *(−∞,∞)

Find the Domain 3x-2y=-16

3*x−2*y=6

Domain: *(−∞,∞)

Find the Domain 3x-2y=6

3*x−4*y=12

Domain: *(−∞,∞)

Find the Domain 3x-4y=12

3*x+4*y=12

Domain: *(−∞,∞)

Find the Domain 3x+4y=12

3*x+y=6

Domain: *(−∞,∞)

Find the Domain 3x+y=6

−3*y=5*x−7

Domain: *(−∞,∞)

Find the Domain -3y=5x-7

3*x+18=50

Domain:(−∞,∞)

Find the Domain 3x+18=50

3*x+2*y=12

Domain: *(−∞,∞)

Find the Domain 3x+2y=12

2*x−6⋅5

(−∞,∞)

Find the Domain 2x-6*5

3+x*i=(x+1)+2*i

Domain:x∈ℝ

Find the Domain 3+xi=(x+1)+2i

−3*(5−6*x)=6−(4*x−(7*x−(6*x−(3*x+33))))

Domain: *(−∞,∞)

Find the Domain -3(5-6x)=6-(4x-(7x-(6x-(3x+33))))

3*t6*(8*t(−6))

Domain: *(−∞,0)∪(0,∞)

Find the Domain 3t^6*(8t^-6)

−4=5*n+6

Domain: *(−∞,∞)

Find the Domain -4=5n+6

4*x+2*y=8

8* is *(−∞,∞)

Find the Domain 4x+2y=8

3*x−y=6

Domain: *(−∞,∞)

Find the Domain 3x-y=6

4*x

Domain: *(−∞,∞)

Find the Domain 4x

4*x+2*y=0

Domain:(−∞,∞)

Find the Domain 4x+2y=0

4*x−2*y=4

(−∞,∞)

Find the Domain 4x-2y=4

4*x−y=5

Domain:(−∞,∞)

Find the Domain 4x-y=5

4*x−5*y=20

Domain:(−∞,∞)

Find the Domain 4x-5y=20

59=4+5*(n−1)

Domain: *(−∞,∞)

Find the Domain 59=4+5*(n-1)

5*x+2*y=7

Domain: *(−∞,∞)

Find the Domain 5x+2y=7

5*x−2*y=−10

Domain: *(−∞,∞)

Find the Domain 5x-2y=-10

5*x=10

Domain: *(−∞,∞)

Find the Domain 5x=10

50=2*w+1

Domain: *(−∞,∞)

Find the Domain 50=2w+1

4*x−y=0

Domain: *(−∞,∞)

Find the Domain 4x-y=0

5*x−y=38

Domain: *(−∞,∞)

Find the Domain 5x-y=38

−6*y2−7*y=2

Domain: *(−∞,∞)

Find the Domain -6y^2-7y=2

y=5*x−10

Domain: *(−∞,∞)

Find the Domain y=5x-10

y=−9

Domain: *(−∞,∞)

Find the Domain y=-9

y=3*x−5

Domain: *(−∞,∞)

Find the Domain y=3x-5

y=3*x−6

Domain:(−∞,∞)

Find the Domain y=3x-6

y=4*x+12

Domain: *(−∞,∞)

Find the Domain y=4x+12

y=4*x+4

Domain: *(−∞,∞)

Find the Domain y=4x+4

y=−4*x+4

Domain: *(−∞,∞)

Find the Domain y=-4x+4

y=3*x+2

Domain:(−∞,∞)

Find the Domain y=3x+2

y=3*x+3

Domain:(−∞,∞)

Find the Domain y=3x+3

y=3*x+1

Domain: *(−∞,∞)

Find the Domain y=3x+1

y=−3*x2

Domain: *(−∞,∞)

Find the Domain y=-3x^2

y=3*x+4

Domain: *(−∞,∞)

Find the Domain y=3x+4

y=−3*x+5

Domain: *(−∞,∞)

Find the Domain y=-3x+5

y=2*x−1

Domain: *(−∞,∞)

Find the Domain y=2x-1

y=2*x+7

Domain: *(−∞,∞)

Find the Domain y=2x+7

y=3*(1/2)x

Domain: *(−∞,∞)

Find the Domain y=3(1/2)^x

y=3*x2+8

Domain: *(−∞,∞)

Find the Domain y=3x^2+8

y=−3/(2*x)

Domain: *{[x∈ℝ,x≠0]}

Find the Domain y=-3/2x

y=0.5*x+1

Domain:(−∞,∞)

Find the Domain y=0.5x+1

y=10*x−2

Domain:(−∞,∞)

Find the Domain y=10x-2

p=250−5*q

Domain:[0,50]

Find the Domain p=250-5q

y=1/(x+3)

Domain: *(−∞,−3)∪(−3,∞)

Find the Domain y=1x+3

y=−2*(x−1)2−4

Domain: *(−∞,∞)

Find the Domain y=-2(x-1)^2-4

y=2*x2−5*x+4

Domain: *(−∞,∞)

Find the Domain y=2x^2-5x+4

y=1/2*(x−4)2−2

Domain: *(−∞,∞)

Find the Domain y=1/2*(x-4)^2-2

( y =

x + 1

+ 3 )

y=1/(2*x+4)

Domain: *{[x∈ℝ,x≠−2]}

Find the Domain y=1/2x+4

x−y=0

Domain: *(−∞,∞)

Find the Domain x-y=0

y=(x+1)2

Domain: *(−∞,∞)

Find the Domain y=(x+1)^2

y=−1/(3*x)

Domain: *{[x∈ℝ,x≠0]}

Find the Domain y=-1/3x

y=1/(3*x−6)

$\text{Domain: } {x

x \in \mathbb{R}, x \neq 2}$

y=−2/(3*x−3)

$\text{Domain: } {x

x \neq 1}$

y=2/(3*x−3)

$\text{Domain: } {x

x \in \mathbb{R}, x \neq 1}$

y=−1/(2*x−4)

$\text{Domain: } {x

x \in \mathbb{R}, x \neq 2}$

y=1/(2*x−4)

$\text{Domain: } {x

x \in \mathbb{R}, x \neq 2}$

y=1/(5*x)

Domain: *{[x∈ℝ,x≠0]}

Find the Domain y=1/5x

y=−1/5*x+3

Domain: *(−∞,∞)

Find the Domain y=-1/5x+3

y=1/(5*x−4)

(−∞,4/5)∪(4/5,∞)

Find the Domain y=1/5x-4

y=2/(3*x)

Domain: *{[x∈ℝ,x≠0]}

Find the Domain y=2/3x

y=3−5

Domain:(−∞,∞)

Find the Domain y=3^2-5

y=2/(5*x+4)

see full solution →

Find the Domain y=2/5x+4

y=−3/(2*x+3)

see full solution →

Find the Domain y=-3/2x+3

y=−3/4*x+1

Domain: *(−∞,∞)

Find the Domain y=-3/4x+1

y=3/(4*x+2)

see full solution →

Find the Domain y=3/4x+2

y=x2+4*x+7

Domain: *(−∞,∞)

Find the Domain y=x^2+4x+7

y=x2+2*x

Domain: *(−∞,∞)

Find the Domain y=x^2+2x

y=x2−2*x

Domain:(−∞,∞)

Find the Domain y=x^2-2x

y=x2−6*x+5

Domain:(−∞,∞)

Find the Domain y=x^2-6x+5

y=0.05*x+20

Domain: *(−∞,∞)

Find the Domain y=0.05x+20

y=4/(x2+2*x−3)

(−∞,−3)∪(−3,1)∪(1,∞)

Find the Domain y=4/(x^2+2x-3)

s=16*t2+32*t

Domain: *(−∞,∞)

Find the Domain s=16t^2+32t

x+y=6

Domain: *(−∞,∞)

Find the Domain (x+y)=6

−x*(4*x+3)=0

Domain: *(−∞,∞)

Find the Domain -x(4x+3)=0

6*x−2*y=12

Domain: *(−∞,∞)

Find the Domain 6x-2y=12

s=1400*(t−15)+150000

Domain: *(−∞,∞)

Find the Domain s=1400(t-15)+150000

x+2*y=10

Domain:(−∞,∞)

Find the Domain x+2y=10

ƒ(x)=−2*x

Domain: *(−∞,∞)

Find the Domain f(x)=-2x

ƒ(x)=−9*x+2

Domain: *(−∞,∞)

Find the Domain f(x)=-9x+2

h(x)=x2

(−∞,∞)

Find the Domain h(x)x^2

(log_)(x+9)=1−(log_)(x)

Domain:(0,∞)

Find the Domain log of x+9=1- log of x

x+2*y=1

Domain: *(−∞,∞)

Find the Domain x+2y=1

x+3*y=−6

Domain: *(−∞,∞)

Find the Domain x+3y=-6

x+y=12

Domain: *(−∞,∞)

Find the Domain x+y=12

x+y=−3

Domain:(−∞,∞)

Find the Domain x+y=-3

x+y=0

Domain:(−∞,∞)

Find the Domain x+y=0

x+y=1

Domain: *(−∞,∞)

Find the Domain x+y=1

x+y=2

Domain: *(−∞,∞)

Find the Domain x+y=2

x+2*y=6

Domain: *(−∞,∞)

Find the Domain x+2y=6

−x+4*y=4

Domain: *(−∞,∞)

Find the Domain -x+4y=4

x+y=9

Domain: *(−∞,∞)

Find the Domain x+y=9

x=y

Domain:(−∞,∞)

Find the Domain x=y

x−2*y=3

Domain:(−∞,∞)

Find the Domain x-2y=3

x=3*y

3*y⇒(−∞,∞)

Find the Domain x=3y

x=3*y+1

Domain: *(−∞,∞)

Find the Domain x=3y+1

x−2*y=8

Domain:(−∞,∞)

Find the Domain x-2y=8

{[3*a+5*b+2*d=0],[4*a+7*b+5*d=0],[a+b−4*d=0],[2*a+9*b+6*d=0])

0, b=0, d=0$

Solve Using an Inverse Matrix

x−4=0

Domain: *(−∞,∞)

Find the Domain x-4=0

x−7=0

Domain:(−∞,∞)

Find the Domain x-7=0

x−4*y=−8

Domain:(−∞,∞)

Find the Domain x-4y=-8

y−3=y*(x+4)

Domain:{[x∈ℝ,x≠−3]}

Find the Domain y-3=y(x+4)

x−y=6

Domain: *(−∞,∞)

Find the Domain x-y=6

x−y=−6

Domain: *(−∞,∞)

Find the Domain x-y=-6

y+5=2*(x+2)

Domain:(−∞,∞)

Find the Domain y+5=2(x+2)

y=−x−1

Domain: *(−∞,∞)

Find the Domain y=-x-1

[[1,2,−3],[2,−1,4],[4,3,−2]]

see full solution →

[Find Reduced Row Echelon Form [[1,2,-3],[2,-1,4],[4,3,-2]]](https://corca.app/doc/pt8Agt5j1eEHXzK6AWBKw)

[[7,0,4],[0,10,0],[4,0,−8]]

see full solution →

[Find the Eigenvectors/Eigenspace [[7,0,4],[0,10,0],[4,0,-8]]](https://corca.app/doc/pU2vE5NByBuHvcPgCm11j)

ƒ(x)=(2−x)2

Domain: *(−∞,∞)

Find the Domain (2-x)^2

((7*x9)/(3*y2))2

{[(x,y)∈ℝ2,y≠0]}

Find the Domain ((7x^9)/(3y^2))^2

ƒ(x)=(x+4)*(x−4)

Domain: *(−∞,∞)

Find the Domain (x+4)(x-4)

[[3,4],[−2,−4]]

(−1+√(,17))/2,(−1−√(,17))/2

[Find the Eigenvalues [[3,4],[-2,-4]]](https://corca.app/doc/lZzeC54D0t3ZLVoG5i0Pi)

|[4+3*i],[4−2*i],[0−4*i]|

√(,61)

[Find the Norm [[4+3i],[4-2i],[0-4i]]](https://corca.app/doc/KyoVhmNcmv5TgrrtSG2qI)

2*x−y=5

Domain: *(−∞,∞)

Find the Domain 2x-y=5

−4*x+6+(x−5)

Domain: *(−∞,∞)

Find the Domain -4x+6+(x-5)

p(2)=−x3−x2+5*x+5

3

Solve for p p(2)=-x^3-x^2+5x+5

√(,(3−2)2+(−1−(−3)2))

3*i

Simplify square root of (3-2)^2+(-1-(-3)^2)

(−3*b*a4)4

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Find the Domain (-3ba^4)^4

(x2+6*x)/10=x/5

Domain: *(−∞,∞)

Find the Domain (x^2+6x)/10=x/5

(log_5)((4*x−5)2)=6

Domain:{[x∈ℝ,x≠5/4]}

Find the Domain log base 5 of (4x-5)^2=6

(

7+6c

-11=-6 )

(

8x-10

=16 )

1/(x+5)+10/(x2−25)=1

Domain:(−∞,−5)∪(−5,5)∪(5,∞)

Find the Domain 1/(x+5)+10/(x^2-25)=1

|[0+3*i],[4+3*i],[2+0*i],[2−3*i]|

√(,51)

[Find the Norm [[0+3i],[4+3i],[2+0i],[2-3i]]](https://corca.app/doc/JXkubkaHXzm9kGP6YLApP)

Null Space*[[1,−1,3],[5,−4,−4],[7,−6,2]]

see full solution →

[Find the Null Space [[1,-1,3],[5,-4,-4],[7,-6,2]]](https://corca.app/doc/-VSvo-TQY58MOjcV70ImC)

[[a,0,0],[0,b,0],[0,0,c]]

see full solution →

[Find the Inverse [[a,0,0],[0,b,0],[0,0,c]]](https://corca.app/doc/wYVm3MR5FZBC0u6sdwwVa)

y=x+7

Domain: *(−∞,∞)

Find the Domain y=x+7

x+2*y=5

Domain: *(−∞,∞)

Find the Domain x+2y=5

|[4−i],[4−2*i],[2+2*i],[3−3*i]|

3√(,7)

[Find the Norm [[4-1i],[4-2i],[2+2i],[3-3i]]](https://corca.app/doc/HzpmDfWnN9eNQtaeVYe30)

[[2,0,6],[−3,5,−19],[4,1,10],[1,−2,7]]

see full solution →

[Find Reduced Row Echelon Form [[2,0,6],[-3,5,-19],[4,1,10],[1,-2,7]]](https://corca.app/doc/FDgCTeLHiCC4Mc6OJz2GM)

|[3+4*i],[4+4*i],[2+2*i],[4−2*i]|

√(,85)

[Find the Norm [[3+4i],[4+4i],[2+2i],[4-2i]]](https://corca.app/doc/tQIkHLKGw8f-4CczIxEJg)

2*x−y=3

Domain:(−∞,∞)

Find the Domain 2x-y=3

[[1,2,3],[0,4,5],[1,0,6]]

see full solution →

[Find the Cofactor Matrix [[1,2,3],[0,4,5],[1,0,6]]](https://corca.app/doc/3sGxvNVH5R9jI3kk2YqKv)

|[2−3*i],[2−2*i],[1−2*i],[1+0*i]|

3√(,3)

[Find the Norm [[2-3i],[2-2i],[1-2i],[1+0i]]](https://corca.app/doc/7nTjeXx8kHE8g663ML3-6)

x=0

Domain:{0}

Find the Domain x=0

y=4

Domain:(−∞,∞)

Find the Domain y=4^x

y=(x−1)/(x2−4)

Domain: *(−∞,−2)∪(−2,2)∪(2,∞)

Find the Domain y

|[0+0*i],[2−3*i],[1+2*i],[1+0*i]|

√(,19)

[Find the Norm [[0+0i],[2-3i],[1+2i],[1+0i]]](https://corca.app/doc/QUiV6N_rykU4vzogfu95N)

|[2+3*i],[4−i],[3+2*i]|

√(,43)

[Find the Norm [[2+3i],[4-1i],[3+2i]]](https://corca.app/doc/2DIy8AEATjGjAvZ7Ne4Hu)

[[2,0,−2],[−3,5,28],[4,1,1],[1,−2,−11]]

see full solution →

[Find Reduced Row Echelon Form [[2,0,-2],[-3,5,28],[4,1,1],[1,-2,-11]]](https://corca.app/doc/37XU3KBLqQ6VvvJD9s6vP)

y=1/(4*x)

$\text{Domain: } {x

x \in \mathbb{R}, x \neq 0}$

S={[[2],[−1],[3],[4],[2]],[[6],[2],[−1],[3],[4]]}

Linearly Independent

Determine if Linearly Dependent

y=−1/(2*x−1)

Domain: *{[x∈ℝ,x≠1/2]}

Find the Domain y=-1/2x-1

|[3−2*i],[3−2*i],[0−i]|

3√(,3)

[Find the Norm [[3-2i],[3-2i],[0-1i]]](https://corca.app/doc/aG6Oh8TQPIgcg1aapo8lo)

y=5*x+3

Domain: *(−∞,∞)

Find the Domain y=5x+3

y=3*x−7

Domain: *(−∞,∞)

Find the Domain y=3x-7

[[1,1],[0,1]]

see full solution →

[Find the Eigenvectors/Eigenspace [[1,1],[0,1]]](https://corca.app/doc/SFZoal6tA1VPRsW9-NbB4)

y=3*x2

Domain: *(−∞,∞)

Find the Domain y=3x^2

5*x+2*y=10

Domain: *(−∞,∞)

Find the Domain 5x+2y=10

x2−3*x+2=0

Domain: *(−∞,∞)

Find the Domain x^2-3x+2=0

x2+2*x+5=0

Domain:(−∞,∞)

Find the Domain x^2+2x+5=0

2*x+y=6

Domain: *(−∞,∞)

Find the Domain 2x+y=6

2*x+y=7

Domain: *(−∞,∞)

Find the Domain 2x+y=7

(x+6)/12=1/6+(x−5)/7

Domain: *(−∞,∞)

Find the Domain (x+6)/12=1/6+(x-5)/7

2*x=y+8

y+8* is *(−∞,∞)

Find the Domain 2x=y+8

2*x−3*y=4

Domain: *(−∞,∞)

Find the Domain 2x-3y=4

2*x−3*y=6

Domain: *(−∞,∞)

Find the Domain 2x-3y=6

(

6n-9

+3=12 )

−2*x+y=4

Domain: *(−∞,∞)

Find the Domain -2x+y=4

2*x−4*y=7

Domain: *(−∞,∞)

Find the Domain 2x-4y=7

2*x−y=8

Domain: *(−∞,∞)

Find the Domain 2x-y=8

22*y2+10*y−30*y2

Domain: *(−∞,∞)

Find the Domain 22y^2+10y-30y^2

x3+3=64

(−∞,∞)

Find the Domain x^3+3^x=64

ƒ(x,y)=x7+y8+8

Domain:{(x,y)∈ℝ2}

Find the Domain x^7+y^8+8

0.1=3.3−x

Domain: *(−∞,∞)

Find the Domain 0.1=3.3-x

10*x−5*x−3*x=0

Domain: *(−∞,∞)

Find the Domain 10x-5x-3x=0

ƒ(x)=(−3)/(x2−5*x−3)

see full solution →

Find the Domain -3/(x^2-5x-3)

1/3*(6*z+10)

Domain: *(−∞,∞)

Find the Domain 1/3*(6z+10)

2/(x+2)+1/(x+4)=4/(x2+6*x+8)

see full solution →

Find the Domain 2/(x+2)+1/(x+4)=4/(x^2+6x+8)

−1/2+1/(5*w)=−3/7

Domain: *w≠0

Find the Domain -1/2+1/5w=-3/7

A={[[1,2],[3,4]],[[1,2],[12,2]]}

The set *A* is Linearly Independent.

[Determine if Linearly Dependent A={[[1,2],[3,4]],[[1,2],[12,2]]}](https://corca.app/doc/UkxdlHUa4KrDoVXxTLN_O)

2/7*(14*q+7/2)−3*q=9

Domain: *(−∞,∞)

Find the Domain 2/7*(14q+7/2)-3q=9

ƒ(x)=(6−2)/(8+5*x−1)

see full solution →

Find the Domain (6-2)/(8+5x-1)

Domain of (96*x3)/(2*x)

$\text{Domain: } {x

x \in \mathbb{R}, x \neq 0}$

(9*w2−49)/(3*w2−w−14)⋅(7*w2+6*w−16)/(49*w2−64)

see full solution →

Find the Domain

(a*c)/(c*b)=3/2

see full solution →

Find the Domain (ac)/(cb)=3/2

d(k)/d(s())=(−4*s3−10*s+54)/((s2−6*s+16)2)

(−∞,∞)

Find the Domain (dk)/(ds)=(-4s^3-10s+54)/((s^2-6s+16)^2)

s()/4+9=2

Domain: *(−∞,∞)

Find the Domain s/4+9=2

x/4=12

Domain:(−∞,∞)

Find the Domain x/4=12

(3√(,27*x27))/(3*x(−2))⋅((−3*x)3)/(3*x(−1))

Domain: *{[x∈ℝ,x>0]}

Find the Domain

x2+y2=13

Domain:[−√(,13),√(,13)]

Find the Domain x^2+y^2=13

x2+3*x−2

Domain: *(−∞,∞)

Find the Domain x^2+3x-2

[[2,2,2,0],[−2,5,2,1],[8,1,4,−1]]

see full solution →

[Find Reduced Row Echelon Form [[2,2,2,0],[-2,5,2,1],[8,1,4,-1]]](https://corca.app/doc/Irc2TMZo48aIpWGgxu93D)

[[2,−3,−2],[2,1,1],[3,2,1]]

see full solution →

[Find Reduced Row Echelon Form [[2,-3,-2],[2,1,1],[3,2,1]]](https://corca.app/doc/7_BXibpxIRoCXULLlRMgM)

[[3,−2,0],[6,−4,−8],[1,12,−2]]

see full solution →

[Find Reduced Row Echelon Form [[3,-2,0],[6,-4,-8],[1,12,-2]]](https://corca.app/doc/Ul1SIk5cM3ZrMYG5Onu3w)

[[3,−2,0],[8,−3,4],[13,−2,0]]

see full solution →

[Find Reduced Row Echelon Form [[3,-2,0],[8,-3,4],[13,-2,0]]](https://corca.app/doc/wPZwZFaelsN-MyyXECPMf)

[[2,4,−1,−2,2,6],[1,3,2,−7,3,9],[5,8,−7,6,1,4]]

see full solution →

Find Reduced Row Echelon Form

[[−3,−2],[4,4],[5,7]]