The document provides instructions on calculating the determinant of matrices. It begins with an overview of determinants and their properties. It then provides examples of calculating the determinant of 2x2 and 3x3 matrices using expansion by minors and diagonals. The key steps shown are expanding the determinants using the minor of each element, where the sign of each term depends on its position in the matrix.

1. Warm up Each person solve their problem Draw some conclusions about which solutions are equal Generalize your conclusions

2. Sheets Matrices & Geometric Transformations Writing Directions (1 page) Direction Master (Transformations 2) (1 page) Matrices Transformations 3 (2 page) Areas of Transformations (1 page) The Shoelace Algorithm (3 page) The Mall Problem (2 page) Operation Practice (1 page)

3. Finding the determinant of a matrix The determinate of a matrix is a number associated with the matrix. The determinate of matrix A is denoted by | A | You can only find the determinate of a square matrix

4. To find the determinant of a 2 x 2 matrix Example = (3)(2) - (4)(-1) = 6 + 4 = 10 3 -1 4 2

5. Finding the determinant of a 3 x 3 matrix using “expansion by minors” 5 -1 -2 0 3 1 4 1 = 3 0 3 4 1

6. Finding the determinant of a 3 x 3 matrix using “expansion by minors” 5 -1 -2 0 3 1 4 1 = 3 0 3 4 1 - 5 -2 3 1 1

7. Finding the determinant of a 3 x 3 matrix using “expansion by minors” = 3((0)(1)-(4)(3)) – 5((-2)(1)-(1)(3)) +-1((-2)(4)-(1)(0)) = 3(-12) – 5(-5) + -1(-8) = -36+25+8 = -3 5 -1 -2 0 3 1 4 1 = 3 0 3 4 1 - 5 -2 3 1 1 + -1 -2 0 1 4 Note: Signs!

8. Finding the determinant of a 3 x 3 matrix using “diagonals” 3 -2 1 5 0 4 = (3 ·0 ·1 + 5 ·3 ·1 + -1 ·-2 ·4) - (-1 ·0 ·1 + 3 ·3 ·4 + 5 ·-2 ·1) = (0+15+8)-(0+36-10) =(23)-(26) = -3 5 -1 -2 0 3 1 4 1