Multiply the Matrices

Problem

[[6,0,0],[0,5,0],[0,0,2]]*[[2,3,4],[3,5,6],[4,6,7]]

Solution

1. Identify the type of multiplication. The first matrix is a diagonal matrix, which means multiplying it by another matrix scales each row of the second matrix by the corresponding diagonal element.

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

6*(2)+0*(3)+0*(4)=12

6*(3)+0*(5)+0*(6)=18

6*(4)+0*(6)+0*(7)=24

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*(2)+5*(3)+0*(4)=15

0*(3)+5*(5)+0*(6)=25

0*(4)+5*(6)+0*(7)=30

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*(2)+0*(3)+2*(4)=8

0*(3)+0*(5)+2*(6)=12

0*(4)+0*(6)+2*(7)=14

5. Assemble the resulting values into a new 3×3 matrix.

Final Answer

[[6,0,0],[0,5,0],[0,0,2]]*[[2,3,4],[3,5,6],[4,6,7]]=[[12,18,24],[15,25,30],[8,12,14]]

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