w -3 Let A = 2 3 1 1 3 N (a) Find the inverse of A by using (i) the inversion algorithm. (ii) the adjoint method. (b) Use the matrix inverse method and the result of (a) to solve each of the following linear systems. + 3x2 + 2x3 = 2, (1) 2x + 3x2 + *3 = R+1, -9x - 3x, + 9x3 = -2. 3x 3x3 = 1, (ii) 2x - 3x, + K = R+2, 3.X, + 2x, = R+1. (c) Use Cramer's rule to solve the system of linear equations in (b)(ii). 6 4 (d) Use the result of (a) to find the inverse of B = - 3 3 3 (e) Does there exist a 3x3 real matrix C such that C -4C+51, = A? If yes, please exhibit one. Otherwise, explain why such a matrix does not exist. (Note: A real matrix is a matrix of which all entries are real numbers.)