Multiply the Matrices

Problem

[[−3,−2,−7],[0,−9,0],[−1,−9,8]]*[[−1,0,0],[0,−1,0],[0,0,−6]]

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 first row of the product by taking the dot product of the first row of the left matrix with each column of the right matrix.

(−3)*(−1)+(−2)*(0)+(−7)*(0)=3

(−3)*(0)+(−2)*(−1)+(−7)*(0)=2

(−3)*(0)+(−2)*(0)+(−7)*(−6)=42

3. Calculate the second row of the product by taking the dot product of the second row of the left matrix with each column of the right matrix.

(0)*(−1)+(−9)*(0)+(0)*(0)=0

(0)*(0)+(−9)*(−1)+(0)*(0)=9

(0)*(0)+(−9)*(0)+(0)*(−6)=0

4. Calculate the third row of the product by taking the dot product of the third row of the left matrix with each column of the right matrix.

(−1)*(−1)+(−9)*(0)+(8)*(0)=1

(−1)*(0)+(−9)*(−1)+(8)*(0)=9

(−1)*(0)+(−9)*(0)+(8)*(−6)=−48

5. Assemble the results into the final matrix.

Final Answer

[[−3,−2,−7],[0,−9,0],[−1,−9,8]]*[[−1,0,0],[0,−1,0],[0,0,−6]]=[[3,2,42],[0,9,0],[1,9,−48]]

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