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. Pressure in a Liquid - How to Derive Formula

    Jul 02, 22 07:53 AM

    This lesson will show clearly how to derive the formula to find the pressure in a liquid.

    Read More

Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.