Simplify the Matrix

Problem

[[−4,3,−6],[0,2,7],[10,15,−3]]−2*[[−1,2,4],[−2,0,3],[5,−6,1]]

Solution

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

2*[[−1,2,4],[−2,0,3],[5,−6,1]]=[[−2,4,8],[−4,0,6],[10,−12,2]]

2. Subtract the resulting matrix from the first matrix by subtracting corresponding elements.

[[−4−(−2),3−4,−6−8],[0−(−4),2−0,7−6],[10−10,15−(−12),−3−2]]

3. Simplify the arithmetic for each individual entry.

−4+2=−2

3−4=−1

−6−8=−14

0+4=4

2−0=2

7−6=1

10−10=0

15+12=27

−3−2=−5

Final Answer

[[−4,3,−6],[0,2,7],[10,15,−3]]−2*[[−1,2,4],[−2,0,3],[5,−6,1]]=[[−2,−1,−14],[4,2,1],[0,27,−5]]

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