Find the Variables

Problem

15*[[3,−6,5],[2,−1,0],[−4,7,4]]−5*X=30*[[−1,−2,1],[5,5,−4],[−3,−2,10]]

Solution

1. Distribute the scalar 15 into the first matrix by multiplying every element by 15

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

2. Distribute the scalar 30 into the matrix on the right side of the equation.

30*[[−1,−2,1],[5,5,−4],[−3,−2,10]]=[[−30,−60,30],[150,150,−120],[−90,−60,300]]

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,−60,300]]−[[45,−90,75],[30,−15,0],[−60,105,60]]

4. Subtract the corresponding elements of the two matrices.

−5*X=[[−75,30,−45],[120,165,−120],[−30,−165,240]]

5. Solve for X by dividing every element in the resulting matrix by −5

X=[[15,−6,9],[−24,−33,24],[6,33,−48]]

Final Answer

X=[[15,−6,9],[−24,−33,24],[6,33,−48]]

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