Simplify the Matrix

Problem

[[1,8,4,9.7],[3,5,2,10.7],[6,5,3,11.9],[1,4,5,7.6],[5,6,4,10.4]]+[[9,5,11,18.2],[4,1,11,14.9],[11,7,15,19.4],[2,8,23,12.5],[16,1,5,17.1]]+[[8,6,18,17.9],[7,1,14,16.5],[6,3,21,18.2],[1,7,17,10.8],[8,2,18,17.1]]+[[7,5,10,15],[0,0,0,0],[6,5,13,15.9],[1,3,12,10.9],[8,4,5,13.9]]+[[4,4,9,12.4],[3,1,9,12],[9,5,9,13.2],[1,4,14,8.9],[12,2,4,13.7]]

Solution

1. Identify the operation as matrix addition, which requires adding the corresponding elements from each matrix at the same row and column position.

2. Sum the elements in the first column:

1+9+8+7+4=29

3+4+7+0+3=17

6+11+6+6+9=38

1+2+1+1+1=6

5+16+8+8+12=49

3. Sum the elements in the second column:

8+5+6+5+4=28

5+1+1+0+1=8

5+7+3+5+5=25

4+8+7+3+4=26

6+1+2+4+2=15

4. Sum the elements in the third column:

4+11+18+10+9=52

2+11+14+0+9=36

3+15+21+13+9=61

5+23+17+12+14=71

4+5+18+5+4=36

5. Sum the elements in the fourth column:

9.7+18.2+17.9+15+12.4=73.2

10.7+14.9+16.5+0+12=54.1

11.9+19.4+18.2+15.9+13.2=78.6

7.6+12.5+10.8+10.9+8.9=50.7

10.4+17.1+17.1+13.9+13.7=72.2

6. Construct the resulting matrix using the calculated sums.

Final Answer

[[1,8,4,9.7],[3,5,2,10.7],[6,5,3,11.9],[1,4,5,7.6],[5,6,4,10.4]]+[[9,5,11,18.2],[4,1,11,14.9],[11,7,15,19.4],[2,8,23,12.5],[16,1,5,17.1]]+[[8,6,18,17.9],[7,1,14,16.5],[6,3,21,18.2],[1,7,17,10.8],[8,2,18,17.1]]+[[7,5,10,15],[0,0,0,0],[6,5,13,15.9],[1,3,12,10.9],[8,4,5,13.9]]+[[4,4,9,12.4],[3,1,9,12],[9,5,9,13.2],[1,4,14,8.9],[12,2,4,13.7]]=[[29,28,52,73.2],[17,8,36,54.1],[38,25,61,78.6],[6,26,71,50.7],[49,15,36,72.2]]

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