Matrices and Determinants Section 4-4 Matrices and Determinants Objective: To evaluate the determinant of a 3 x 3 matrix. To find the area of a triangle given the coordinates of its vertices.

Determinants Only square matrices have determinants.

Second-Order Determinant -40 – -77 -40 + 77 37

Third-Order Determinant Determinants of 3x3 matrices are called third-order determinants. One method of evaluating third-order determinants is called expansion by minors. The minor of an element is the determinant formed when the row and column containing the element are deleted.

Expansion of a Third-Order Determinant

Example 1 2(40 – 63) – 3(48 – -7) + 4(54 – -5) 2(-23) – 3(55) + 4(59) -46 – 165+ 236 25

Third-Order Determinant Another method for evaluating a third-order determinant is using diagonals. In this method, you begin by writing the first two columns on the right side of the determinant.

Diagonals Method

Example 2

Area of Triangles

Example 3 Find the area of the triangle whose vertices are located at (3, -4), (5, 4), (-3, 2).

Assignment 4-4 pg 209 #11-26 all