1. 4.3 DETERMINANTS AND
CRAMER’S RULE

2. WHAT IS A DETERMINANT?
A special number associated with a
square matrix.
Denoted “det A” or by |A|
Determinant of a 2 x 2 matrix:

3. 2 X 2 EXAMPLES
Evaluate the determinant of the matrix.

4. YOUR TURN!
Evaluate the determinant.

5. DETERMINANT OF A 3 X 3 MATRIX
Rewrite the first 2 columns to the right
of your matrix.
Multiply the diagonals.
Add/Subtract.

6. 3 X 3 EXAMPLE
Evaluate the determinant.

7. YOUR TURN!
Evaluate the determinant.

8. CRAMER’S RULE (2 X 2)
Used to solve linear systems.
Linear System:
Coefficient Matrix: = A
If det A 0,
Replace coefficients for the variable
you are finding with constants.

9. 2 X 2 EXAMPLES
Solve each system using Cramer’s rule.
8x + 5y = 2
2x – 4y = -10
4x – 6y = 4
x + 5y = 14

10. YOUR TURN!
Use Cramer’s rule to solve the system:
9x + 2y = 7
4x – 3y = 42

11. CRAMER’S RULE (3 X 3)
Let A be the coefficient matrix of the system:
If det A 0, then

12. 3 X 3 EXAMPLE
Solve the system using Cramer’s rule.
x + 3y – z = 1
-2x – 6y + z = -3
3x + 5y – 2z = 4