Math 9.5 Matrix Review Solution Key

Pre-Calculus 9.5 Matrix Review HW Worksheet Use the following matrices to perform the indicated operation, if possible. (ALL NON-CALCULATOR). Circle your answer please. Use extra paper if necessary, and attach it to this sheet. This will be turned in on Friday, Nov. 1   18th at the beginning of the hour. A = [5 -2] B = [0 -3] C = [4 1] D = [6] E = [0 6] F = [1 -6] [3 4] [1 -7] [1 2] [3] [0 4] [0 1] 1. A + E [9 2] [3 12] 2. -3C + 2B [-12 0 -12] [ 9 -35 1] 3. B - 6C [-24 -9 -6] [ 7 -49 -4] 4. 2A + 3C impossible 5. AE [20 -46] [-12 50] 6. ED [6] [24] 7. CF + A [29 2] [-21 5] 8. B^2 impossible 9. AB [9 -1 -26] [-4 -19 -10] A = [3 -5] B = [0 -3] C = [4 1] D = [6] E = [0 6] F = [1 -6] [4 2] [1 -7] [1 2] [3] [0 4] [0 1] 10. E^2 [16 24] [ 0 64] 11. CD impossible 12. DC impossible Find the value of x and y. 13. [3x y+6] = [-12 -3] [ 0 5 ] [ y+9 5 ] x = -4 y = -9 14. [x+6 3y] = [-4 3^2] [36 2y-1] = [6^2 15] x = -10 y = 24 Solve the matrix equation for the unknown matrix X where: A = [2 1] B = [1 -2] [3 2] [2 4] 15. A + 3X = B X = [-1/3 -1] [-6/3 2/3] 16. 1/2(X - 2B) = A X = [6 -2] [2 12] 2. -3C + 2B = [-12 -6 0] [ 3 -21 -3] 3B = [0 6 -12] [-1 14 4] 1. AE = [-5 2] [0 6] = [3 4] [0 4] 2x2 2x2 2x2 R1C1 = -5(0) + 2(0) = 0 R1C2 = -5(6) + 2(4) = -20 R2C1 = 3(0) + 4(0) = 0 R2C2 = 3(6) + 4(4) = 12 6. ED = [6] [1 -6] = [3] [0 8] 2x1 1x2 = 2x1 R1C1 = (6)(-1) + (3)(0) = -6 R2C1 = (0)(-1) + (8)(0) = 0 7. CF + A = [4 1] [1 0] = [1 2] [0 5] 2x2 2x2 2x2 R1C1 = 4(1) + 1(0) = 4 R1C2 = 4(0) + 1(5) = 5 R2C1 = 1(-1) + 2(0) = -1 R2C2 = 1(-6) + 2(5) = 4 9. AB = [5 -2] [0 3 -6] [3 4] [1 2 7] 2x2 2x3 2x3 R1C1 = -5(0) + (-2)(1) = -2 R1C2 = -5(3) + (-2)(-7) = -1 R1C3 = -5(-6) + (-2)(2) = 26 R2C1 = 3(0) + 4(1) = 4 R2C2 = 3(3) + 4(-7) = -19 R2C3 = 3(-6) + 4(7) = -10 10. E^2 = [4 -6] [4 -6] [0 8] [0 8] 2x2 2x2 2x2 R1C1 = (4)(-4) + (-6)(0) = -16 R1C2 = (4)(-6) + (-6)(8) = -72 R2C1 = (0)(-4) + (8)(0) = 0 R2C2 = (0)(-6) + (8)(8) = 64 15. A + 3X = B 3X = B - A X = 1/3 (B - A) [x y] = 1/3 [[1 -2] - [2 1]] [-2 4] [3 2] X = [-1/3 -1] [-2/3 2/3] 16. 1/2(X - 2B) = A X - 2B = 2A X = 2A + 2B 2A = [4 2] [6 4] 2B = [2 -4] [-4 8] 2A + 2B = [6 -2] [-2 12]