(a) For each of the following systems; write the matrix equation and the augmented form of the system and solve the system with any method of your choice: i. ii. (b) Evaluate the determinant 13x + 4y = 51 32x5y = -12 7x 12y = 216 6x + 15y = 329 1 0 4 3 5-1 0 1 2 (3 marks) (d) Describe all solutions to the following equations in parametric form: i. 3x-y + 2z = 6 ii. 3x1x2 + 2x3 + 4x4 = 10 iii. 3x2 + 4x3 = 9 - iv. 1-5x2 + 4x3 = (e) Differentiate between dimension and rank of a matrix. (3 marks) i. with the help of second row, ii. with the help of the third column. (c) Find a cubic polynomial y = ar + bx + cr+d which passes through the point (1,3) with slope -5 and through the point (3,-7) with slope - 1. (4 marks) (4 marks) (10 marks) (3 marks) (4 marks) (3 marks) (3 marks) (2 marks) (f) Show that the set Fmxn of all mxn matrices over a field F is a vector space over F with respect to the addition of matrices as vector addition and multiplication of a matrix by a scalar as scalar multiplication. (10 marks)