Find the Kernel

Problem

2*X+[[2,−3],[−9,0],[8,9]]=[[4,1],[5,−4],[8,1]]

Solution

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

2*X=[[4,1],[5,−4],[8,1]]−[[2,−3],[−9,0],[8,9]]

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

2*X=[[4−2,1−(−3)],[5−(−9),−4−0],[8−8,1−9]]

3. Simplify the resulting matrix.

2*X=[[2,4],[14,−4],[0,−8]]

4. Divide every entry of the matrix by 2 to solve for X

X=1/2*[[2,4],[14,−4],[0,−8]]

5. Calculate the final values for each entry.

X=[[1,2],[7,−2],[0,−4]]

Final Answer

X=[[1,2],[7,−2],[0,−4]]

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