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Problem

−7*[[1,4],[8,−3],[7,−8]]−4*[[−9,8],[−4,−2],[−9,−7]]

Solution

1. Distribute the scalar −7 into the first matrix by multiplying every element by −7

−7*[[1,4],[8,−3],[7,−8]]=[[−7,−28],[−56,21],[−49,56]]

2. Distribute the scalar −4 into the second matrix by multiplying every element by −4

−4*[[−9,8],[−4,−2],[−9,−7]]=[[36,−32],[16,8],[36,28]]

3. Add the two resulting matrices by summing the corresponding elements in each position.

[[−7+36,−28−32],[−56+16,21+8],[−49+36,56+28]]

4. Simplify the arithmetic for each element to find the final matrix.

[[29,−60],[−40,29],[−13,84]]

Final Answer

−7*[[1,4],[8,−3],[7,−8]]−4*[[−9,8],[−4,−2],[−9,−7]]=[[29,−60],[−40,29],[−13,84]]

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