Find the Variables [[a+b,c+d],[c-d,a-b]]=[[4,6],[10,2]]

Problem

[[a+b,c+d],[c−d,a−b]]=[[4,6],[10,2]]

Solution

1. Set up equations by equating the corresponding elements of the two matrices.

a+b=4

c+d=6

c−d=10

a−b=2

2. Solve for a and b by adding the first and fourth equations.

(a+b)+(a−b)=4+2

2*a=6

a=3

3. Substitute a back into the first equation to find b

3+b=4

b=1

4. Solve for c and d by adding the second and third equations.

(c+d)+(c−d)=6+10

2*c=16

c=8

5. Substitute c back into the second equation to find d

8+d=6

d=−2

Final Answer

a=3,b=1,c=8,d=−2

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