Multiply the Matrices

Problem

[[1,2,5],[2,4,7],[5,7,6]]*[[4,0,0],[0,3,0],[0,0,2]]

Solution

1. Identify the type of multiplication. The second matrix is a diagonal matrix, which means multiplying the first matrix by it on the right will scale each column of the first matrix by the corresponding diagonal element.

2. Calculate the first column of the resulting matrix by multiplying the first column of the left matrix by the first diagonal element, 4

1⋅4=4

2⋅4=8

5⋅4=20

3. Calculate the second column of the resulting matrix by multiplying the second column of the left matrix by the second diagonal element, 3

2⋅3=6

4⋅3=12

7⋅3=21

4. Calculate the third column of the resulting matrix by multiplying the third column of the left matrix by the third diagonal element, 2

5⋅2=10

7⋅2=14

6⋅2=12

5. Combine the calculated columns into the final matrix format.

Final Answer

[[1,2,5],[2,4,7],[5,7,6]]*[[4,0,0],[0,3,0],[0,0,2]]=[[4,6,10],[8,12,14],[20,21,12]]

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