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Problem

−1/3*[[−5],[7],[1],[0]]+1/2*[[−2],[−4],[0],[1]]

Solution

1. Distribute the scalar −1/3 into the first vector by multiplying it with each component.

[[5/3],[−7/3],[−1/3],[0]]

2. Distribute the scalar 1/2 into the second vector by multiplying it with each component.

[[−1],[−2],[0],[1/2]]

3. Add the corresponding components of the two resulting vectors.

[[5/3+(−1)],[−7/3+(−2)],[−1/3+0],[0+1/2]]

4. Simplify each component by finding common denominators where necessary.

[[2/3],[−13/3],[−1/3],[1/2]]

Final Answer

−1/3*[[−5],[7],[1],[0]]+1/2*[[−2],[−4],[0],[1]]=[[2/3],[−13/3],[−1/3],[1/2]]

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