Find the Variables

Problem

2*X+[[−4,−2],[−6,1],[1,4]]=[[−6,−6],[0,−1],[−1,−4]]

Solution

1. Isolate the term containing the matrix X by subtracting the constant matrix from both sides of the equation.

2*X=[[−6,−6],[0,−1],[−1,−4]]−[[−4,−2],[−6,1],[1,4]]

2. Subtract the corresponding elements of the two matrices on the right side.

2*X=[[−6−(−4),−6−(−2)],[0−(−6),−1−1],[−1−1,−4−4]]

3. Simplify the resulting matrix.

2*X=[[−2,−4],[6,−2],[−2,−8]]

4. Divide every element in the matrix by 2 to solve for X

X=1/2*[[−2,−4],[6,−2],[−2,−8]]

5. Calculate the final values for each entry in matrix X

X=[[−1,−2],[3,−1],[−1,−4]]

Final Answer

X=[[−1,−2],[3,−1],[−1,−4]]

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