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] 

Recent Articles

  1. How To Find The Factors Of 20: A Simple Way

    Sep 17, 23 09:46 AM

    Positive factors of 20
    There are many ways to find the factors of 20. A simple way is to...

    Read More

  2. The SAT Math Test: How To Be Prepared To Face It And Survive

    Jun 09, 23 12:04 PM

    SAT math
    The SAT Math section is known for being difficult. But it doesn’t have to be. Learn how to be prepared and complete the section with confidence here.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes