4.5 Determinants of Matrices 1 2x2 Matrices 2 3x3 Matrices 3 Practice Problems www.themegallery.com

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

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

Example Find the value of the determinant of

Another Example Find the value of the determinant of

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

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

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

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

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