Question

13. Given the following matrices, what is the correct product matrix CD?ABсD(2] [] [507]1oThe product matrix is undefined.[29 53][53 29](21 10]

Answer 1

[ 53 29]

Step-by-step explanation:

To find the product matrix CD we need to find the dot product of each row of C with each column of D.

Where the dot product of two vectors is equal to:

`\lbrack a\text{ b c\rbrack }\cdot\lbrack d\text{ e f\rbrack = ad + be+ cf}`

Therefore, the dot product of each row of C by each column of D is equal to:

[5 9 7] [ 2 4 1 ] = 5(2) + 9(4) + 7(1)

[5 9 7] [ 2 4 1 ] = 10 + 36 + 7

[5 9 7] [ 2 4 1 ] = 53

[5 9 7] [ -4 0 7 ] = 5(-4) + 9(0) + 7(7)

[5 9 7] [ -4 0 7 ] = -20 + 0 + 49

[5 9 7] [ -4 0 7 ] = 29

Therefore, the correct product matrix is:

[ 53 29]