4.7 Solving Systems with Matrices
November 07, 2008
4.7 Solving Systems Using Matrices
Objective: Solve a system of two equations using matrices
Oct 31­7:59 AM
1
4.7 Solving Systems with Matrices
November 07, 2008
Check Skills You'll Need
Oct 31­8:03 AM
2
4.7 Solving Systems with Matrices
November 07, 2008
Nov 1­8:26 PM
3
4.7 Solving Systems with Matrices
November 07, 2008
Write each system as a matrix equation
1.
2.
Nov 1­8:35 PM
4
4.7 Solving Systems with Matrices
November 07, 2008
Solve the system using matrices and a graphing calculator
A
_
A 1A
B
We cannot divide matrices, so in order to solve for the variable matrix, we multiply both sides of the equation by the inverse of matrix A.
Multiplying a mtrix by its inverse equals 1.
Solving this operation gives us the solution to the system of equations. This is what we put into our calculator to solve.
Nov 1­8:35 PM
5
4.7 Solving Systems with Matrices
November 07, 2008
Solve the system using matrices and a graphing calculator
1 3
2 ­4
7
24
First, locate the matrix button on the calculator.
Nov 1­8:35 PM
6
4.7 Solving Systems with Matrices
November 07, 2008
Solve the system using matrices and a graphing calculator
1 3
2 ­4
7
24
To input matrix A, go to edit
Enter the dimension of the matrix you wish to input
Enter the values of matrix A. Press enter to move to the next element. When finished, press quit.
Nov 1­8:35 PM
7
4.7 Solving Systems with Matrices
November 07, 2008
Solve the system using matrices and a graphing calculator
1 3
2 ­4
7
24
Repeat those steps to enter matrix B Nov 1­8:35 PM
8
4.7 Solving Systems with Matrices
November 07, 2008
Solve the system using matrices and a graphing calculator
1 3
2 ­4
7
24
Now, we need to retreive those matrices
Select matrix A under names Press the inverse key
Nov 1­8:35 PM
9
4.7 Solving Systems with Matrices
November 07, 2008
Solve the system using matrices and a graphing calculator
1 3
2 ­4
7
24
Select matrix B
Press Enter
This is the variable matrix
x = 10
y = ­1
Nov 1­8:35 PM
10
4.7 Solving Systems with Matrices
November 07, 2008
Solve the system of equations using matrices
Nov 1­8:39 PM
11
4.7 Solving Systems with Matrices
November 07, 2008
Homework
pg. 217
#'s:1­3, 7­12
Oct 31­8:15 AM
12