(a) Solve each of the following systems using the Cramer's Rule only. i. ii. (b) If...
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(a) Solve each of the following systems using the Cramer's Rule only. i. ii. (b) If A = 3x1 " 2x1 1 x₂ + x3 = 5 12x2 + 3x3 = 15 - 3x3 = 4 x₁ + x₂ - 13 = 3 x₂ + 4x3 = 2 3x1 + x₂ 1 2 2 2 1 2 2 2 1, matrix and the null matrix of order 3 respectively. Use this result to find A-¹. = 5 show show that A² - 4A-51 = 0, where I, 0 are the unit (d) Define the term linear transformation and show that the function T: R² defined by = T(V₁, V₂) (V₁ V2, V₁ +20₂) (c) If a certain number is added to both the numerator and denominator of a given fraction, its value is. However, if the same number is subtracted from both the numerator and denominator, its value is . If, however, 1 is added to both numerator and denominator, the fraction is. Find the fraction. - (8 marks) cos - sin sin cos (0) (8 marks) is a linear transformation. (e) Find all solutions of the homogeneous system 3z + x + 2y = 0 4x + 6z + 5y = 0 8y + 7x = 0 (f) Show that the linear transformation T: R² R³ represented by the matrix (6 marks) (5 marks) → R² (6 marks) (7 marks) has the property that it rotates every vector in R2 counterclockwise about the origin through the angle 0. (5 marks) (a) Solve each of the following systems using the Cramer's Rule only. i. ii. (b) If A = 3x1 " 2x1 1 x₂ + x3 = 5 12x2 + 3x3 = 15 - 3x3 = 4 x₁ + x₂ - 13 = 3 x₂ + 4x3 = 2 3x1 + x₂ 1 2 2 2 1 2 2 2 1, matrix and the null matrix of order 3 respectively. Use this result to find A-¹. = 5 show show that A² - 4A-51 = 0, where I, 0 are the unit (d) Define the term linear transformation and show that the function T: R² defined by = T(V₁, V₂) (V₁ V2, V₁ +20₂) (c) If a certain number is added to both the numerator and denominator of a given fraction, its value is. However, if the same number is subtracted from both the numerator and denominator, its value is . If, however, 1 is added to both numerator and denominator, the fraction is. Find the fraction. - (8 marks) cos - sin sin cos (0) (8 marks) is a linear transformation. (e) Find all solutions of the homogeneous system 3z + x + 2y = 0 4x + 6z + 5y = 0 8y + 7x = 0 (f) Show that the linear transformation T: R² R³ represented by the matrix (6 marks) (5 marks) → R² (6 marks) (7 marks) has the property that it rotates every vector in R2 counterclockwise about the origin through the angle 0. (5 marks)
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Contemporary Business Mathematics with Canadian Applications
ISBN: 978-0134141084
11th edition
Authors: S. A. Hummelbrunner, Kelly Halliday, Ali R. Hassanlou, K. Suzanne Coombs
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