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Problem

5*[[8,3],[4,−7],[−8,−5]]+7*[[5,−2],[8,4],[4,−4]]

Solution

1. Perform scalar multiplication on the first matrix by multiplying every entry by 5

5*[[8,3],[4,−7],[−8,−5]]=[[40,15],[20,−35],[−40,−25]]

2. Perform scalar multiplication on the second matrix by multiplying every entry by 7

7*[[5,−2],[8,4],[4,−4]]=[[35,−14],[56,28],[28,−28]]

3. Add the resulting matrices by summing the corresponding entries from each matrix.

[[40+35,15+(−14)],[20+56,−35+28],[−40+28,−25+(−28)]]

4. Simplify the arithmetic to find the final matrix entries.

[[75,1],[76,−7],[−12,−53]]

Final Answer

5*[[8,3],[4,−7],[−8,−5]]+7*[[5,−2],[8,4],[4,−4]]=[[75,1],[76,−7],[−12,−53]]

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