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]