Simplify the Matrix

Problem

[[0,1,0,2],[1,−1,−2,2],[0,1,3,−3],[−2,2,3,−2]]+[[0,−1,0,−2],[−1,1,2,−2],[0,−1,−3,3],[2,−2,−3,2]]+[[1,3,−2,−1],[−3,−12,10,6],[0,−2,2,1],[−2,−6,5,3]]

Solution

1. Add the first two matrices by summing their corresponding entries.

[[0+0,1−1,0+0,2−2],[1−1,−1+1,−2+2,2−2],[0+0,1−1,3−3,−3+3],[−2+2,2−2,3−3,−2+2]]=[[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]]

2. Observe that the first two matrices are additive inverses of each other, resulting in the zero matrix.

3. Add the resulting zero matrix to the third matrix.

[[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]]+[[1,3,−2,−1],[−3,−12,10,6],[0,−2,2,1],[−2,−6,5,3]]=[[1,3,−2,−1],[−3,−12,10,6],[0,−2,2,1],[−2,−6,5,3]]

Final Answer

[[0,1,0,2],[1,−1,−2,2],[0,1,3,−3],[−2,2,3,−2]]+[[0,−1,0,−2],[−1,1,2,−2],[0,−1,−3,3],[2,−2,−3,2]]+[[1,3,−2,−1],[−3,−12,10,6],[0,−2,2,1],[−2,−6,5,3]]=[[1,3,−2,−1],[−3,−12,10,6],[0,−2,2,1],[−2,−6,5,3]]

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