Using Matrices to Solve a 3-Variable System

(A Must be a square matrix) Inverse Matrix The product of a square matrix A and its inverse matrix A-1, on the left or the right, is the identity matrix I. AA-1= A-1A =I (A Must be a square matrix) How do we find the Inverse Matrix:

Converting a Systems of Equations to a Matrix Equation Make sure the equations are in alphabetical order Identify all of the coefficients to the variables Coefficient Matrix Variable Matrix Constant Matrix

Solving a Systems of Equations with Matrices Solve: Identify all of the coefficients to the variables Make sure the equations are in alphabetical order and that every variable is in each equation Coefficient Matrix “A” Variable Matrix “X” Constant Matrix “B”

Solving a Systems of Equations with Matrices Continued… A X B Which Order is Correct? Multiply by the inverse of A to isolate the variable matrix 3x3.3x1 A-1 A X A-1 B 3x1.3x3 OR A-1 A X B A-1

Solving a Systems of Equations with Matrices Continued… A X B Step 1: Store Matrix A and B in your calculator Multiply by the inverse of A to isolate the variable matrix A-1 A X A-1 B Step 2: Enter this in your calculator to solve the system THUS: You do not need to calculate the inverse matrix! If… Then…