Question

Please help with this question

Answer 1

c.

Explanation:

You want a linear combination of the given 3×3 matrices.

Strategy

We observe that the answer choices are different in most corresponding terms, so we only need to find the value of one term in order to choose the correct answer.

Linear combination

The expression applied to the matrices is applied to corresponding terms of the matrices. That is, for ...

`C = -2A +7B`

you will have ...

`c_(11)=-2a_(11)+7b_(11)\\\\c_(11)=-2(4)+7(7)=-8+49\\\\c_(11)=41`

This matches choice c.

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Additional comment

Many graphing calculators and all spreadsheets can do the necessary calculations to help you find the desired result matrix.