A matrix is a rectangular array of numbers.  Addition and subtraction of matrices involve adding and subtracting numbers in the same position in each matrix.  Multiplication of matrices involve multiplying numbers in each row of the first matrix by numbers in each column of the second.  The size (dimension) of a matrix is the number of rows by number of columns. 

Consider the following system of equations. 

The coefficient matrix is , the variable matrix is, and the constant matrix is  . The system can be rewritten as 

₌

Compare this to the equation 5x = 7.  How do we solve this equation?  We divide both sides by 5, or multiply by the inverse of 5.  On the left side, we get just the variable, and we have the inverse of 5 times 7.  Speaking in math terms, x equals the inverse of the coefficient times the constant.  Likewise, the answer to the above equation is 

₌^-1

^{Finding the inverse of a matrix is a greater task, but we can let the graphing calculator help us with that.  See the sequence of steps in the graphs on the left.} 
 

Graphing Calculator Explorations
1.   Solve the system of linear equations by using the inverse matrix method.  4.3x - 2.1y  = 8.6 32x + 15y = 11.2        2.   Use the inverse matrix method to solve the system of linear equations.  3x - 4y + 5z = 12 2x + 3y - 2z = 16 4x - 11y - z = -10