# Solve a matrix equation

The way to solve a matrix equation is to follow the same procedure for solving linear equations. You can use the subtraction and addition properties of equality to solve the matrix.

Example #1:

Solve X - [5   2   1] = [-1   2   4]

Notice that X represents a matrix. A matrix equation is basically an equation in which the variable is a matrix. Notice also that [5   2   1] and [-1   2   4] are 1 x 3 matrices. Therefore X is a 1 x 3 matrix as well.

X - [5   2   1] = [-1   2   4]

Add [5   2   1] to each side of the equation.

X - [5   2   1] + [5   2   1] = [-1   2   4] + [5   2   1]

X + [-5   -2   -1] + [5   2   1] = [-1   2   4] + [5   2   1]

X + [-5+5   -2+2   -1+1] = [-1+5   2+2   4+1]

X + [0   0   0] = [4   4   5]

X  = [4   4   5]

Example #2:

Solve X + [-1   2   -5] = [2   2   3]

Subtract [-1   2   -5] from each side of the equation.

X + [-1   2   -5] - [-1   2   -5] = [2   2   3] - [-1   2   -5]

X + [-1   2   -5] + [1   -2   5] = [2   2   3] + [1   -2   5]

X + [-1+1   2+-2   -5+5] = [2+1   2+-2   3+5]

X + [0   0   0] = [3   0   8]

X = [3   0   8]

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