Determine if Linear

Problem

X−[[0,1,5,−6],[5,8,7,−1]]=[[1,2,3,6],[−8,−4,−2,−3]]

Solution

1. Identify the equation as a linear matrix equation of the form X−A=B where X A and B are matrices of the same dimension.

2. Isolate the variable matrix X by adding matrix A to both sides of the equation.

X=[[1,2,3,6],[−8,−4,−2,−3]]+[[0,1,5,−6],[5,8,7,−1]]

3. Perform matrix addition by adding the corresponding elements from each matrix.

X=[[1+0,2+1,3+5,6+(−6)],[−8+5,−4+8,−2+7,−3+(−1)]]

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

X=[[1,3,8,0],[−3,4,5,−4]]

Final Answer

X=[[1,3,8,0],[−3,4,5,−4]]

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