1.10 and 1.11

1. 1.10 and 1.11 Quiz 1.10-1.11: Friday Matrices Test: Oct. 20

2. Determinants • Associated with each square matrix (n x n) is a real number called its determinant. • The determinant of matrix A is denoted by det A or by |A|.

3. Determinant of a 2 x 2 matrix:

4. Determinant of a 3 x 3 matrix:

5. Example 1: • Evaluate the determinants:

6. Identity Matrix

7. Inverses • Two n x n matrices A and B are inverses of each other if their product is the n x n identity matrix. • That is, AB = I and BA = I • An n x n matrix only has an inverse if and only if the determinant is NOT zero • We denote the inverse of A with A-1

8. Inverse of a 2 x 2 matrix:

9. Example 3: • Find the inverse of

10. We will use our calculator to find the inverse of a 3 x 3 • Find the inverse of

11. Matrix Equation Variable matrix, X Constant matrix, B Coefficient matrix, A AX = B

12. Matrix Equation AX = B A-1(AX) = A-1B (A-1A)X = A-1B IX = A-1B X = A-1B

13. Example 4:

14. Example 5: use your calculator • Solve using matrices: 5x + 2y – z =-7 x - 2y + 2z =0 3y + z =17 X = -2 Y = 4 Z = 5

15. Homework: GREEN BOOK (M3) • P. 51 # 1-6 • P. 57 #1-17odd