Multiply the Matrices

Problem

[[2,3,5],[3,4,6],[5,6,7]]*[[6,0,0],[0,4,0],[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 results in scaling each column of the first matrix by the corresponding diagonal element.

2. Calculate the first column of the product by multiplying the first column of the left matrix by 6

2⋅6=12

3⋅6=18

5⋅6=30

3. Calculate the second column of the product by multiplying the second column of the left matrix by 4

3⋅4=12

4⋅4=16

6⋅4=24

4. Calculate the third column of the product by multiplying the third column of the left matrix by 2

5⋅2=10

6⋅2=12

7⋅2=14

5. Combine the results into a single matrix.

Final Answer

[[2,3,5],[3,4,6],[5,6,7]]*[[6,0,0],[0,4,0],[0,0,2]]=[[12,12,10],[18,16,12],[30,24,14]]

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