Determine if Linear

Problem

15*[[3,−6,5],[2,−1,0],[−4,7,4]]−5*x=30*[[−1,−2,1],[5,5,−4],[−3,−2,1]]

Solution

1. Multiply the first matrix by the scalar 15 by multiplying each entry by 15

15*[[3,−6,5],[2,−1,0],[−4,7,4]]=[[45,−90,75],[30,−15,0],[−60,105,60]]

2. Multiply the second matrix by the scalar 30 by multiplying each entry by 30

30*[[−1,−2,1],[5,5,−4],[−3,−2,1]]=[[−30,−60,30],[150,150,−120],[−90,−60,30]]

3. Isolate the term −5*x by subtracting the first matrix from both sides of the equation.

−5*x=[[−30,−60,30],[150,150,−120],[−90,−60,30]]−[[45,−90,75],[30,−15,0],[−60,105,60]]

4. Subtract the matrices by subtracting corresponding entries.

−5*x=[[−75,30,−45],[120,165,−120],[−30,−165,−30]]

5. Divide every entry by −5 to solve for x

x=[[15,−6,9],[−24,−33,24],[6,33,6]]

Final Answer

x=[[15,−6,9],[−24,−33,24],[6,33,6]]

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