Multiply the Matrices

Problem

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

Solution

1. Identify the dimensions of the matrices. Both are 3×3 matrices, so the resulting matrix will also be 3×3

2. Calculate the elements of the first row by multiplying the first row of the left matrix by each column of the right matrix.

(c_11)=(−3)*(−3)+(0)*(1)+(0)*(−3)=9

(c_12)=(−3)*(0)+(0)*(−1)+(0)*(−4)=0

(c_13)=(−3)*(0)+(0)*(0)+(0)*(−4)=0

3. Calculate the elements of the second row by multiplying the second row of the left matrix by each column of the right matrix.

(c_21)=(1)*(−3)+(−1)*(1)+(0)*(−3)=−3−1=−4

(c_22)=(1)*(0)+(−1)*(−1)+(0)*(−4)=1

(c_23)=(1)*(0)+(−1)*(0)+(0)*(−4)=0

4. Calculate the elements of the third row by multiplying the third row of the left matrix by each column of the right matrix.

(c_31)=(−3)*(−3)+(−4)*(1)+(−4)*(−3)=9−4+12=17

(c_32)=(−3)*(0)+(−4)*(−1)+(−4)*(−4)=4+16=20

(c_33)=(−3)*(0)+(−4)*(0)+(−4)*(−4)=16

5. Assemble the resulting matrix using the calculated values.

Final Answer

[[−3,0,0],[1,−1,0],[−3,−4,−4]]*[[−3,0,0],[1,−1,0],[−3,−4,−4]]=[[9,0,0],[−4,1,0],[17,20,16]]

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