Question 1 Let A be the matrix: A = NIN -6 where a is a constant. (a) Assume that A has no inverse, Show that a must be 8 [6 marks] (b) Consider the system of simultaneous equations: 2x + By + 42 - b; -x +4y + 2z = -2: 2x - 6y - 32 = 4. where b is a constant. Given that the system has solutions, use row reduction to find all possible values of b. [6 marks] (c) Assume instead that A has eigenvector c ( ! ) where c is a constant. Find the eigenvalue associated with this eigenvector, and then show that a must be 5 [6 marks] (d) Suppose x. y). yz and y, satisfy: dyz dys dx dyl = 2y1 + 5/2 + 4/3: dx -y +42 + 2y3: dx = 21 - 6y2 - 3y3- Two of the three terms in the general solution of y. ) and yo are given: Given that y (0) = 3. )(0) = 1 and ys(0) = -8, find yr. )2 and ys. [7 marks]