1. WUPS: Find the determinates by hand
Name: _____________
WUPS: Find the determinates by hand 1.
3.8 Warm-ups 2.
Corrected By: ______________________________

2. 4.5 Use Inverse Matrices to Solve Matrix Equations
By the end you should:
1. find the inverse of a 2 x 2 and 3 x 3 matrix
2. solve a matrix equation
Identity Matrix: a square matrix (n x n) with 1's as its main diagonal and
zeros everywhere else.
2 x 2 IM
If a matrix is
multiplied by an
identity matrix, then
you will get the
matrix. Similar to
multiplying a number
by one.
3 x 3 IM

3. Inverse Matrices
1) 2 matrices are inverses of each other if their product (in both orders) equals the identity matrix. ex. AB = I and BA = I
a matrix can only have an inverse if it is square
its determinant does not equal zero (Remember: you
may NEVER divide by 0)

4. Inverse of a 2x2 Matrix
The Inverse of matrix is

5. ….to find the inverse of a matrix (2 x 2)
Let’s try some:

6. ….to find the inverse of a 3 x 3 matrix using your calculator
On your calculator…..
Enter the 3 x 3 matrix
Select matrix from the home screen
Press ENTER
What do you get?

7. Solve a Matrix Equation
How would you normally solve for x? AX = B
When you have a matrix you cannot “divide” by a matrix, so you take the ________________.

8. Your turn: solve the matrix equation

9. Solve a Linear System Solve the following linear system: 2x – 3y = 19
Step 1: write as a matrix equation AX = B
coefficient · matrix of = matrix of
matrix (A) variables (X) constants (B)
Step 2: find the inverse of A
Step 3: solve for X

10. Your turn: 1. -2x + 3y = -11 5x + y = 19 2. 4x + y = 10 3x + 5y = -1
Calculator:
Enter A and B
Your turn:
1. -2x + 3y = -11
5x + y = 19
2. 4x + y = 10
3x + 5y = -1
3. –x – 2y + 4z = -28
x + y + 2z = -11
2x + y – 3z = 30

11. Yeah….more word problems!
At a video store, the cost of 3 DVDs, 2 video games, and 4 VHS movies is $130. The cost of 2 DVDs, 1 video game, and 5 VHS movies is $105. The cost of 3 DVDs, 3 video games, and 3 VHS movies is $135. Find the cost of each item.

12. …you must be able to solve by hand!!!
Homework: 3.8 pg. 214 (3-29 odd, 35-37, 44)
**** Do #3-11 SOLVE BY HAND
Show ALL your work
Beware...
…you must be able to solve by hand!!!

13. Find the inverse BY HAND
Exit Card Name: ________________________
Find the inverse BY HAND
Solve the system of linear equations using matrices
3x – 2y = 5
6x – 5y = 14