1. Matrices Chapter 6

2. Warmup – Solve Trig Equations Unit 5.3 Page 327 Solve 4sinx = 2sinx + √2 1.2sinx = √2 Subtract 2sinx from both sides 2.Sinx = √2/2 Divide 2 from both sides A.Work on the following problems Unit 5.3 Page 331 Problems 1, 3, 4, 9, 10

3. Chapter 6: Matrices What are matrices? Rectangular array of mn real or complex numbers arranged in m horizontal rows and n vertical columns rows 2 3 4 7 1 5 6 1 0 columns

4. Matrices: Why should I care? 1. Matrices are used everyday when we use a search engine such as Google: Example: Airline distances between cities LondonMadridNYTokyo London07853469 5959 Madrid78503593 6706 NY346935930 6757 Tokyo5959 6706 6757 0

5. Quick Review Unit 6.1 Page 372 Problems 1 - 4

6. Write an Augmented Matrix Unit 6.1 Page 366 Guided Practice 2a w + 4x + 0y + z = 2 1 4 0 1 2 0w + x + 2y – 3z = 0 0 1 2 -3 0 w + 0x – 3y – 8z = -1 1 0 -3 -8 -1 3w +2x + 3y + 0z = 9 3 2 3 0 9 Page 372 Problems 9 - 14

7. Row Echelon Form Objective: Solve for several variables 1 a b c 0 1 d e 0 0 1 f The first entry in a row with nonzero entries is 1, or leading 1 For the next successive row, the leading 1 in the higher row is farther to the left than the leading 1 in the lower row

8. Row Echelon form Unit 6.1 Page 372 Problems 16 - 21

9. Gauss-Jordan Elimination How do I solve for each variable? x + 2y – 3z = 7 -3x - 7y + 9z = -12 2x + y – 5z = 8 Augmented 1 2 -3 7 -3 -7 9 -12 2 1 -5 8

10. Gauss-Jordan Elimination 1.Use the following steps on your graphing calculator 2 nd →matrix Edit Select A Choose Dimensions (row x column) Enter numbers 2 nd → quit 2 nd →matrix Math Rref (reduced reduction echelon form) 2 nd Matrix → select

11. Gauss-Jordan Elimination Unit 6.1 Page 372 Problems 24 - 28

12. Multiplying with matrices 3 Types a.Matrix addition (warm-up) b.Scalar multiplication c.Matrix multiplication

13. Adding matrices 1.Only one rule, both rows and columns must be equal 1.If one matrix is a 3 x 4, then the other matrix must also by 3 x 4 Which of the following matrix cannot be added? A B C D 2 x 4 7 x 810 x 1114 x 12 3 x 47 x 810 x 1114 x 12

14. Scalar Multiplication {-2 1 3} 4 -6 = { (-2)4 + 1(-6) + 3(5) } = {1} 5

15. Multiplying Matrices In order for matrices to be multiplied, the number of columns in matrix A, must equal the number of rows in matrix B. Matrix AMatrix B 3 x 22 x 4 equal New proportions

16. Multiplying Matrices Procedures – row times column A B 3-1 -2 0 6 40 3 5 1 3 (-2) + (-1)3 3(0) + -1(5) (3)(6) + (-1)1 4(-2) +(0)3 4(0) + 0(5)4(6) + (0)1 Answer-9 -517 -8 024

17. Unit 6.2 Page 383 Problems 1 – 8 1. Determine if the matrices can be multiplied, then computer A x B

18. Unit 6.2 Problems 1 – 8, 19 - 26