Add

Problem

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

Solution

1. Identify the corresponding elements in each matrix. Matrix addition is performed by adding the elements in the same row and column positions.

2. Add the elements of the first row: 1+5 2+7 3+(−9) and 4+4

1+5=6

2+7=9

3−9=−6

4+4=8

3. Add the elements of the second row: −2+0 −3+3 −4+1 and −5+(−1)

−2+0=−2

−3+3=0

−4+1=−3

−5−1=−6

4. Add the elements of the third row: 0+4 3+6 2+(−8) and 1+7

0+4=4

3+6=9

2−8=−6

1+7=8

5. Add the elements of the fourth row: −1+5 2+0 −2+3 and 0+4

−1+5=4

2+0=2

−2+3=1

0+4=4

6. Construct the resulting matrix using the sums calculated in the previous steps.

Final Answer

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

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