Determinants Objectives 1 To find the determinant of

Determinants Objectives: 1. To find the determinant of a 2 x 2 and a 3 x 3 matrix 1. To find the area of a triangle in the coordinate plane using determinants

Warm-Up Let’s say you’re programming software for a camera to allow the camera to determine who is in the image. What is one thing the camera needs to look at to determine that your face is in an image?

Objective 1 You will be able to find the determinant of a 2 x 2 and a 3 x 3 matrix

Exercise 1 • Pick a segment as the base Find height

Exercise 1 • 2. Surround with a large rectangle Find area of large rectangle Subtract areas of unshaded right triangles

Exercise 1 • 2. Surround with a large rectangle This is an application of the determinant of a matrix

Determinant The determinant of a square matrix is simply a real number that is associated with that matrix. A determinant determines or identifies something. We’ll see exactly what this is shortly.

2 x 2 Determinant

Exercise 2 •

Exercise 3 Evaluate the determinant of each matrix.

Exercise 4 •

3 x 3 Determinant Diagonals Method: This one is a little crazier. First you have to duplicate the first two columns and then write them after the last column.

3 x 3 Determinant Diagonals Method: Now find the sum of the products of the major diagonal elements. Finally subtract the sum of the products of the minor diagonal elements.

Exercise 5 •

Determinants (3 x 3) Expansion by Minors:

Exercise 6 •

Objective 2 You will be able to find the area of a graphed triangle using determinants

Area of a Triangle Finding the area of a triangle in the coordinate plane is as easy as taking half of the determinant an augmented matrix.

Area of a Triangle • The extra credit for this six weeks is to prove this. It’s worth 5 points on your six weeks grade. Check website for more details.

Exercise 7 Find the area of ABC.