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4.2 Adding and Subtracting Matrices

4.2 Adding and Subtracting Matrices. Adding and Subtracting Matrices Solving Matrix Equations. 1) Adding and Subtracting Matrices. The Rules… Addition and subtraction can only be done with matrices that have the same dimensions Add or subtract corresponding matrix elements.

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4.2 Adding and Subtracting Matrices

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  1. 4.2 Adding and Subtracting Matrices Adding and Subtracting Matrices Solving Matrix Equations

  2. 1) Adding and Subtracting Matrices The Rules… • Addition and subtraction can only be done with matrices that have the same dimensions • Add or subtract corresponding matrix elements

  3. 1) Adding and Subtracting Matrices Example 1: Find the sum. 1 2 3 2 -1 -9 3 4 5 4 7 1 +

  4. 1) Adding and Subtracting Matrices Example 1: Find the sum. 1 2 32 -1 -9 3 4 54 7 1 + Add corresponding elements.

  5. 1) Adding and Subtracting Matrices Example 1: Find the sum. 1 2 32 -1 -9 3 4 54 7 1 =1 + 2 2 – 1 3– 9 3+ 4 4+ 7 5+ 1 +

  6. 1) Adding and Subtracting Matrices Example 1: Find the sum. 1 2 32 -1 -9 3 4 54 7 1 =1 + 2 2 – 1 3– 9 = 3 1 -6 3+ 4 4+ 7 5+ 1 7 11 6 +

  7. 1) Adding and Subtracting Matrices Example 2: Find each sum. (a) [1 -3 4] + [0 0 0] (b) [-2 6 4] + [2 -6 -4]

  8. 1) Adding and Subtracting Matrices Example 2: Find each sum. • [1 -3 4] + [0 0 0] (b) [-2 6 4] + [2 -6 -4] = [1 + 0-3 + 04 + 0] = [1 -3 4]

  9. 1) Adding and Subtracting Matrices Example 2: Find each sum. • [1 -3 4] + [0 0 0] (b) [-26 4] + [2 -6 -4] = [1 + 0-3 + 04 + 0] = [-2 + 26 – 6 4 – 4] = [1 -3 4] = [0 0 0]

  10. 1) Adding and Subtracting Matrices Example 2: Find each sum. • [1 -3 4] + [0 0 0] (b) [-26 4] + [2 -6 -4] = [1 + 0-3 + 04 + 0] = [-2 + 26 – 6 4 – 4] = [1 -3 4] = [0 0 0] Adding a zero matrix does not change the original matrix

  11. 1) Adding and Subtracting Matrices Example 2: Find each sum. • [1 -3 4] + [0 0 0] (b) [-26 4] + [2 -6 -4] = [1 + 0-3 + 04 + 0] = [-2 + 26 – 6 4 – 4] = [1 -3 4] = [0 0 0] Adding a zero matrix does An additive inverse creates not change the original matrix a zero matrix These matrices are opposites.

  12. 2) Solving Matrix Equations Example 1:Solve for the matrix X. 1 4 2 4 -2 3 3 8 X - =

  13. 2) Solving Matrix Equations Example 1: Solve for the matrix X. 1 4 2 4 -2 3 3 8 2 4 1 4 3 8 -2 3 = X - X = +

  14. 2) Solving Matrix Equations Example 1: Solve for the matrix X. 1 4 2 4 -2 3 3 8 2 41 4 3 8-2 3 X - = X = +

  15. 2) Solving Matrix Equations Example 1: Solve for the matrix X. 1 4 2 4 -2 3 3 8 2 41 4 3 8-2 3 2 + 14 + 4 3 – 28 + 3 = X - + X = X =

  16. 2) Solving Matrix Equations Example 1: Solve for the matrix X. 1 4 2 4 -2 3 3 8 2 41 4 3 8-2 3 2 + 14 + 4 3 – 28 + 3 3 8 1 11 = X - X = + X = X =

  17. 2) Solving Matrix Equations Example 2: Solve for the matrix B. 5B = 40 35

  18. 2) Solving Matrix Equations Example 2: Solve for the matrix B. 5B = 40 35 B = 8 7

  19. 2) Solving Matrix Equations Example 3: Solve the equationx + 8 -5 38 -5 for x and y. 3 -y 3 4y – 10 =

  20. 2) Solving Matrix Equations Example 3: Solve the equationx + 8 -5 38 -5 for x and y. 3 -y 3 4y – 10 Assume the two matrices are equal. If true, corresponding elements are equal. =

  21. 2) Solving Matrix Equations Example 3: Solve the equationx + 8 -5 38 -5 for x and y. 3 -y 3 4y – 10 Assume the two matrices are equal. If true, corresponding elements are equal. =

  22. 2) Solving Matrix Equations Example 3: Solve the equationx + 8 -5 38 -5 for x and y. 3 -y 3 4y – 10 Assume the two matrices are equal. If true, corresponding elements are equal. =

  23. 2) Solving Matrix Equations Example 3: Solve the equationx + 8 -5 38 -5 for x and y. 3 -y 3 4y – 10 x + 8 = 38 =

  24. 2) Solving Matrix Equations Example 3: Solve the equationx + 8 -5 38 -5 for x and y. 3 -y 3 4y – 10 x + 8 = 38 x = 38 – 8 x = 30 =

  25. 2) Solving Matrix Equations Example 3: Solve the equationx + 8 -5 38 -5 for x and y. 3 -y 3 4y – 10 x + 8 = 38 -y = 4y – 10 x = 38 – 8 x = 30 =

  26. 2) Solving Matrix Equations Example 3: Solve the equationx + 8 -5 38 -5 for x and y. 3 -y 3 4y – 10 x + 8 = 38 -y = 4y – 10 x = 38 – 8 10 = 4y + y x = 302 = y =

  27. 2) Solving Matrix Equations Example 3: Solve the equationx + 8 -5 38 -5 for x and y. 3 -y 3 4y – 10 x + 8 = 38 -y = 4y – 10 x = 38 – 8 10 = 4y + y x = 302 = y The solutions are x = 30 and y = 2. =

  28. 2) Solving Matrix Equations Example 4: Solve each equation for x and y. [3x 4] = [-9 x + y]

  29. 2) Solving Matrix Equations Example 4: Solve each equation for x and y. [3x4] = [-9x + y]

  30. 2) Solving Matrix Equations Example 4: Solve each equation for x and y. [3x4] = [-9x + y] 3x = -9 x = -3

  31. 2) Solving Matrix Equations Example 4: Solve each equation for x and y. [3x4] = [-9x + y] 3x = -9 4 = x + y x = -34 = -3 + y 7 = y

  32. 2) Solving Matrix Equations Example 4: Solve each equation for x and y. [3x4] = [-9x + y] 3x = -9 4 = x + y x = -34 = -3 + y 7 = y The solutions are x = -3 and y = 7.

  33. Homework p.178 #1-5, 10, 11, 16-19, 26, 28 QUIZ – Friday October 30 Section 4.1 …bring your supplies…I will NOT be providing anything

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