complete all

3 Let A = 2 3 3 (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. + 3.x, + 2x3 2. (i) 2x, + 3x, + * = R+1, - 3x, + -2 3.x 1, (ii) 2x 3.X2 + = R+2, - 3X, + 2x3 = R+1. (c) Use Cramer's rule to solve the system of linear equations in (b)(ii). 6 4 2 (d) Use the result of (a) to find the inverse of B = 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.)