(a) Solve each of the following systems using the Cramer's Rule only. i. ii. (b) If A = 3x1 " 2x1 1 x + x3 = 5 12x2 + 3x3 = 15 - 3x3 = 4 x + x - 13 = 3 x + 4x3 = 2 3x1 + x 1 2 2 2 1 2 2 2 1, matrix and the null matrix of order 3 respectively. Use this result to find A-. = 5 show show that A - 4A-51 = 0, where I, 0 are the unit (d) Define the term linear transformation and show that the function T: R defined by = T(V, V) (V V2, V +20) (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: R R represented by the matrix (6 marks) (5 marks) R (6 marks) (7 marks) has the property that it rotates every vector in R2 counterclockwise about the origin through the angle 0. (5 marks)