Simplify the Matrix -1[[2],[-1]]-1[[-1],[2]]

Problem

−1*[[2],[−1]]−1*[[−1],[2]]

Solution

1. Distribute the scalar −1 into the first vector by multiplying each component by −1

−1*[[2],[−1]]=[[−2],[1]]

2. Distribute the scalar −1 into the second vector by multiplying each component by −1

−1*[[−1],[2]]=[[1],[−2]]

3. Add the two resulting vectors by summing their corresponding components.

[[−2],[1]]+[[1],[−2]]=[[−2+1],[1+(−2)]]

4. Simplify the arithmetic to find the final vector components.

[[−1],[−1]]

Final Answer

−1*[[2],[−1]]−1*[[−1],[2]]=[[−1],[−1]]

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