(a) Solve each of the following systems using the Cramer's Rule only. i. ii. (b) Evaluate the determinant 3x12x2 + 4x3 = 1 -2x1 - x + x3 = -3 6x14x2 + 8x3 = 2 + 2x 3x3 = 6 2x14x2 - 6x3 = 7 -X - 2x3 = 5 3x1 - log3 512 log, 3 log, 8 log 9 100 22 1 -2 (8 marks) (c) Find the characteristic polynomial, characteristic equation and the characteristic roots for the following matrix: -2 1 (8 marks) (4 marks) (6 marks) (4 marks) (d) Describe all solutions to 3x-y + 2z = 6 in parametric form. (e) Determine constants a, b and c so that the parabola y = ax + bx+c will pass through the points (1,3), (0,5) and (3,11). (6 marks) (f) Solve the following system of linear equations by Gauss-Jordan Elimination method: x3 + 4 = 1 + 2x2 21+472 + 3x3 = 5 673 +7= 1 + 2x2 (7 marks)