Answer each of the following: (a) A matrix polynom is given by P(x) = xª. By considering the 2 by 2 matrix as A = [1 2], find P(A). (b) For a given matrix A = [2], calculate A-t, where k is any integer. Q. 3) (15 p.) The inverse of a matrix can be applied to the solution of nonhomogeneous linear equations. (a) Prove the theorem: If the system AX = B, where A shows nonsingular and has a unique solution, then the solution is given by X = A-¹B. (b) Solve the linear equation system by following the above theorem, and verify your result. x + y + z = 2 x + 0 + z = 0 2 x - y + 0 = 2