1. 4.5 Determinants of Matrices1
2x2 Matrices 2
3x3 Matrices 3
Practice Problems

2. Definitions Determinant
A square array of numbers between two parallel lines
aka a square matrix
Can also be represented by a single number

3. 2 x 2 Matrix Determinants (Second Order)
Steps
Multiply the upper left element by the lower right element
Multiply the upper right element by the lower left element
Subtract the second value from the first

4. Example
Find the value of the determinant of

5. Another Example
Find the value of the determinant of

6. 3 x 3 Matrix Determinants (Third Order)
Expansion by minors
A minor of an element is the determinant formed when the row and column containing that element are deleted

7. 3 x 3 Matrix Determinants (Third Order)
Expansion by minors (Cont.)
The sign (negative or positive)of a minor is determined by its position in the matrix

8. Evaluating a Matrix Using Expansion by Minors
Steps
Each member of one row is multiplied by its minor and its position sign
The 2x2 minors are evaluated
Simplify

9. Example of Evaluating a Matrix Using Expansion by Minors
Evaluate using expansion by minors.

10. Practice Problems Page 185 Problems 7-13, 15-26, 27-32
Odd problems due today
Even problems due by next class