a. Consider the linear system of equations: 3x - y + z = 0 x + 2y +2z = 0 4x + 1+ 32 = 0 i. Find the determinant of the coefficient matrix A. Is a unique solution of the linear system possible? Explain. 2 marks ii. Solve the linear system. 3 marks b. Explain whether or not the following linear system has non trivial solutions. 1 mark 2x1 - 3X2 + 4x3 - X4 = 0 7x, + x2 - 8x, + 9x, = 0 2x] + 8x, + X3 - X, = 0 c. Determine the value(s) of b for which the matrix A = [5-b -1 6 - 2 - b is singular. 2 marks -1 -3 d. Consider the augmented matrix A = 3 2 1 6 2 2 i. Use elementary row operations to reduce the matrix A to its reduced row echelon form. 4 marks ii. Determine the rank(A). 1 mark iii. Is the associated linear system consistent? Explain your answer in terms of the ranks of the coefficient matrix and augmented matrix. 1 mark