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Problem

−5*([[−2,2],[3,−3],[1,4]]+[[5,1],[−1,6],[8,2]])

Solution

1. Add the corresponding elements of the two matrices inside the parentheses.

[[−2,2],[3,−3],[1,4]]+[[5,1],[−1,6],[8,2]]=[[−2+5,2+1],[3−1,−3+6],[1+8,4+2]]

2. Simplify the resulting matrix sums.

[[3,3],[2,3],[9,6]]

3. Multiply every element of the resulting matrix by the scalar −5

−5*[[3,3],[2,3],[9,6]]=[[−5*(3),−5*(3)],[−5*(2),−5*(3)],[−5*(9),−5*(6)]]

4. Calculate the final values for each entry.

[[−15,−15],[−10,−15],[−45,−30]]

Final Answer

−5*([[−2,2],[3,−3],[1,4]]+[[5,1],[−1,6],[8,2]])=[[−15,−15],[−10,−15],[−45,−30]]

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