Using Matrices to Solve a 3-Variable System

1
Using Matrices to Solve a 3-Variable System
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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
3
Converting a Systems of Equations to a
Matrix Equation
Identify all of the coefficients to the variables
Make sure the equations are in alphabetical order
Variable Matrix
Constant Matrix
Coefficient Matrix
4
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
Variable Matrix X
Constant Matrix B
Coefficient Matrix A
5
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
A-1
X
B
A-1
3x1.3x3
OR
A
A-1
X
B
A-1
6
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
A-1
X
B
A-1
Step 2 Enter this in your calculator to solve
the system
THUS
You do not need to calculate the inverse matrix!
If
Then