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Matrices

Matrices. Chapter 6. Warmup – Solve Trig Equations. Unit 5.3 Page 327 Solve 4sinx = 2sinx + √2 2sinx = √2 Subtract 2sinx from both sides Sinx = √2/2 Divide 2 from both sides Work on the following problems Unit 5.3 Page 331 Problems 1, 3, 4, 9, 10. Chapter 6: Matrices.

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Matrices

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  1. Matrices Chapter 6

  2. Warmup – Solve Trig Equations • Unit 5.3 Page 327 Solve 4sinx = 2sinx + √2 • 2sinx = √2 Subtract 2sinx from both sides • Sinx = √2/2 Divide 2 from both sides • 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 London Madrid NY Tokyo London 0 785 3469 5959 Madrid 785 0 3593 6706 NY 3469 3593 0 6757 Tokyo 5959 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 • 2 -3 7 -3 -7 9 -12 2 1 -5 8

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

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

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

  13. Adding matrices • Only one rule, both rows and columns must be equal • 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 8 10 x 11 14 x 12 3 x 4 7 x 8 10 x 11 14 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 A Matrix B • 3 x 2 2 x 4 • equal • New proportions

  16. Multiplying Matrices Procedures – row times column A B • -1 -2 0 6 • 0 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 -5 17 -8 0 24

  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

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