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 Coefficient matrix, A Variable matrix, X Constant matrix, B AX = B

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

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