Simplify the Matrix 3[[3,4],[6,-2]]+2[[2,-4],[-1,5]]

Problem

3*[[3,4],[6,−2]]+2*[[2,−4],[−1,5]]

Solution

1. Distribute the scalar 3 into the first matrix by multiplying every element by 3

3*[[3,4],[6,−2]]=[[9,12],[18,−6]]

2. Distribute the scalar 2 into the second matrix by multiplying every element by 2

2*[[2,−4],[−1,5]]=[[4,−8],[−2,10]]

3. Add the two resulting matrices by adding their corresponding elements.

[[9,12],[18,−6]]+[[4,−8],[−2,10]]=[[9+4,12−8],[18−2,−6+10]]

4. Simplify the arithmetic to find the final matrix.

[[13,4],[16,4]]

Final Answer

3*[[3,4],[6,−2]]+2*[[2,−4],[−1,5]]=[[13,4],[16,4]]

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