1. Do Now: Solve the system of linear equations using matrices (Row Echelon Form)

2. Academy Algebra II/Trig
12.3: Systems of linear equations: Determinants, 12.4: Inverses
Unit 3 Test: Thurs, 10/31 ( , 12.7)

3. Finding the Determinant for a 2 x 2
Given
Then
gives you the determinant.

4. Find the determinant of the matrix.
1.)
2.)

5. Cramer's Rule
Cramer’s Rule can be used to solve a system of equations when the det = 0.
Given the system:
Using Cramer’s Rule, the solution to the system is given by:

6. Solve the system using Cramer’s Rule.
1.)
2.)

7. Finding the Determinant of a 3x3

8. Evaluate.

9. Solve the system using Cramer’s Rule.

10. 12.4: Inverse Matrices
Two matrices are inverses of each other if their product = identity matrix.
The inverse of a 2x2 matrix is
Note: Matrix A will not have an inverse if
the determinant = 0.

11. Find the inverse of the matrix, if possible.
1.)
2.)

12. Finding the Inverse for a 3 x 3
You will find inverses for a 3 x 3 matrix
on the calculator.
Input the following matrix by creating a new matrix or overwriting a current matrix.
Note: Once you are entering #’s in the cells for the matrix you can resize the matrix by selecting the Util menu (F6) – option 6.

13. Finding the Inverse for a 3 x 3
You will find inverses for a 3 x 3 matrix
on the calculator.
Input the following matrix by creating a new matrix or overwriting a current matrix.
Press Home.
Type the name of your matrix and raise it to the -1 exponent. Press ENTER.

14. Finding the determinant on calculator
You can also find determinants for a matrix
on the calculator.
To find the determinant for this matrix – on your home screen complete the following:
Go to MATH menu (Press 2nd 5)
Select Matrix, select det(
Enter the name of your matrix, close parenthesis. Press ENTER.

15. Using inverse matrices to solve a linear system.
Given system:

16. Solve the system using Inverses.

17. Solve the system using Inverses.