Simplify the Matrix

Problem

3*[[−2,−1],[1,0],[3,−4]]−2*[[0,3],[2,0],[−4,−1]]

Solution

1. Perform scalar multiplication on the first matrix by multiplying every entry by 3

3*[[−2,−1],[1,0],[3,−4]]=[[−6,−3],[3,0],[9,−12]]

2. Perform scalar multiplication on the second matrix by multiplying every entry by 2

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

3. Subtract the matrices by subtracting the corresponding entries of the second matrix from the first.

[[−6−0,−3−6],[3−4,0−0],[9−(−8),−12−(−2)]]

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

[[−6,−9],[−1,0],[17,−10]]

Final Answer

3*[[−2,−1],[1,0],[3,−4]]−2*[[0,3],[2,0],[−4,−1]]=[[−6,−9],[−1,0],[17,−10]]

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