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Problem

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

Solution

1. Identify the corresponding elements in each matrix. To add two matrices, they must have the same dimensions, and you add the entries that are in the same row and column.

2. Add the elements in the first row:

5+(−1)=4

1+(−3)=−2

3. Add the elements in the second row:

1+(−3)=−2

−9+(−3)=−12

4. Add the elements in the third row:

6+4=10

7+2=9

5. Combine these results into a new matrix of the same dimensions (3×2.

Final Answer

[[5,1],[1,−9],[6,7]]+[[−1,−3],[−3,−3],[4,2]]=[[4,−2],[−2,−12],[10,9]]

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