Simplify the Matrix

Problem

−2*[[9,7],[−4,2],[−5,−9]]+3*[[−5,−2],[−6,9],[8,−8]]

Solution

1. Distribute the scalar −2 into the first matrix by multiplying every element by −2

−2*[[9,7],[−4,2],[−5,−9]]=[[−18,−14],[8,−4],[10,18]]

2. Distribute the scalar 3 into the second matrix by multiplying every element by 3

3*[[−5,−2],[−6,9],[8,−8]]=[[−15,−6],[−18,27],[24,−24]]

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

[[−18+(−15),−14+(−6)],[8+(−18),−4+27],[10+24,18+(−24)]]

4. Simplify the arithmetic to find the final values for each entry.

[[−33,−20],[−10,23],[34,−6]]

Final Answer

−2*[[9,7],[−4,2],[−5,−9]]+3*[[−5,−2],[−6,9],[8,−8]]=[[−33,−20],[−10,23],[34,−6]]

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