Simplify the Matrix

Problem

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

Solution

1. Distribute the scalar 4 into the first matrix by multiplying every entry by 4

4*[[3,−6],[−1,8],[−3,3]]=[[12,−24],[−4,32],[−12,12]]

2. Distribute the scalar 5 into the second matrix by multiplying every entry by 5

5*[[8,−1],[−3,−3],[−2,−3]]=[[40,−5],[−15,−15],[−10,−15]]

3. Add the two resulting matrices by summing the corresponding entries.

[[12+40,−24−5],[−4−15,32−15],[−12−10,12−15]]

4. Simplify the arithmetic for each entry to find the final matrix.

[[52,−29],[−19,17],[−22,−3]]

Final Answer

4*[[3,−6],[−1,8],[−3,3]]+5*[[8,−1],[−3,−3],[−2,−3]]=[[52,−29],[−19,17],[−22,−3]]

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