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Problem

2*[[1,2,3,4],[−2,−3,−4,−5],[0,3,2,1],[−1,2,−2,0]]+3*[[5,7,−9,4],[0,3,1,−1],[4,6,−8,7],[5,0,3,4]]

Solution

1. Perform scalar multiplication on the first matrix by multiplying every element by 2

2*[[1,2,3,4],[−2,−3,−4,−5],[0,3,2,1],[−1,2,−2,0]]=[[2,4,6,8],[−4,−6,−8,−10],[0,6,4,2],[−2,4,−4,0]]

2. Perform scalar multiplication on the second matrix by multiplying every element by 3

3*[[5,7,−9,4],[0,3,1,−1],[4,6,−8,7],[5,0,3,4]]=[[15,21,−27,12],[0,9,3,−3],[12,18,−24,21],[15,0,9,12]]

3. Add the matrices by summing the corresponding elements from each resulting matrix.

[[2+15,4+21,6−27,8+12],[−4+0,−6+9,−8+3,−10−3],[0+12,6+18,4−24,2+21],[−2+15,4+0,−4+9,0+12]]

4. Simplify the sums to find the final matrix.

[[17,25,−21,20],[−4,3,−5,−13],[12,24,−20,23],[13,4,5,12]]

Final Answer

2*[[1,2,3,4],[−2,−3,−4,−5],[0,3,2,1],[−1,2,−2,0]]+3*[[5,7,−9,4],[0,3,1,−1],[4,6,−8,7],[5,0,3,4]]=[[17,25,−21,20],[−4,3,−5,−13],[12,24,−20,23],[13,4,5,12]]

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