Multiply the Matrices

Problem

[[8,0,0],[0,−7,0],[0,0,−2]]*[[3,4],[6,−9],[−1,7]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 3×3 diagonal matrix and the second is a 3×2 matrix. The resulting matrix will be 3×2

2. Calculate the first row of the product by multiplying the first row of the diagonal matrix by each column of the second matrix.

8*(3)+0*(6)+0*(−1)=24

8*(4)+0*(−9)+0*(7)=32

3. Calculate the second row of the product by multiplying the second row of the diagonal matrix by each column of the second matrix.

0*(3)+(−7)*(6)+0*(−1)=−42

0*(4)+(−7)*(−9)+0*(7)=63

4. Calculate the third row of the product by multiplying the third row of the diagonal matrix by each column of the second matrix.

0*(3)+0*(6)+(−2)*(−1)=2

0*(4)+0*(−9)+(−2)*(7)=−14

5. Assemble the results into the final 3×2 matrix.

Final Answer

[[8,0,0],[0,−7,0],[0,0,−2]]*[[3,4],[6,−9],[−1,7]]=[[24,32],[−42,63],[2,−14]]

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