1. For the following matrices, compute the rank. If the matrix is invertible, compute the inverse. (a) (b) 1 2 0 1 1 2 4 1 3 0 A = 3 6 2 5 1 -81 - 2 -410 2 0 -1 1 -3, 2. For the given linear transformation T, find [T]s, the rank of T, the inverse of [T]s, and use [T] to construct T-. = T: P((R))P(R), T(f(x))"(2)+2f'(2) - (2), 8-(1,2,2) 3. Express the matrix A and its inverse A-1 as a product of elementary matrices. 4. Find all solutions to the following systems. x1 x2- x3=-1 (a) (1 3 O A = 0 0 5 3 10 0 (b) 4x1+x22x3 = 3 - x1+2+3x3x4 = 0 1+2+3+x4 = 1 x12x2+3x41 - 4x1+2+8x3 - 4 = 0 5. For the system of linear equations, find the solution by appropriate matrix multiplication by A-1, the inverse matrix of the coefficient matrix A. 1+2+3 = 1 - 2x1 2x2+3 = 4 x1+2x2 x3 = 5 6. (Revision Token for correct solutions.) Let A be invertible. By Gauss-Jordan Elimination, find the inverse of a A == cd 2). Ensure you are not dividing by zero.