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Problem

2*[[1/2,−1/2],[−1/2,1/2]]+4*[[1/2,1/2],[1/2,1/2]]

Solution

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

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

2. Distribute the scalar 4 into the second matrix by multiplying every element by 4

4*[[1/2,1/2],[1/2,1/2]]=[[2,2],[2,2]]

3. Add the two resulting matrices by adding their corresponding entries.

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

4. Simplify the arithmetic for each entry.

[[3,1],[1,3]]

Final Answer

2*[[1/2,−1/2],[−1/2,1/2]]+4*[[1/2,1/2],[1/2,1/2]]=[[3,1],[1,3]]

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