Solve the Matrix Equation

Problem

−3*X+[[7,0,−1],[2,−3,4]]=[[10,0,8],[−19,−18,10]]

Solution

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

−3*X=[[10,0,8],[−19,−18,10]]−[[7,0,−1],[2,−3,4]]

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

−3*X=[[10−7,0−0,8−(−1)],[−19−2,−18−(−3),10−4]]

−3*X=[[3,0,9],[−21,−15,6]]

3. Solve for X by dividing every element in the resulting matrix by −3

X=−1/3*[[3,0,9],[−21,−15,6]]

X=[[3/(−3),0/(−3),9/(−3)],[(−21)/(−3),(−15)/(−3),6/(−3)]]

4. Simplify the fractions to find the final matrix X

X=[[−1,0,−3],[7,5,−2]]

Final Answer

−3*X+[[7,0,−1],[2,−3,4]]=[[10,0,8],[−19,−18,10]]⇒X=[[−1,0,−3],[7,5,−2]]

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