1. Use Gauss elimination to solve the following systems of equations: (a) 2x1 + 12 - 13 = 1 T1 - 212 + 13 = -c1 + 212 + 13 = 6 (b) 2x1 + 12 - 13 = 3 T1 - 202 + Is = 1 4x1 - 3x2 + 13 = 1 (c) 201 + 12 - 13 + CA =1 X1 - 202 + 13 - TA -x1 + 212 + 23 + 214 = 1 2. Use Gauss-Jordan elimination to solve system (a) in the previous exercise. 3. For each of the following matrices, use Gauss-Jordan elimination to either find its inverse or to show that it is singular (i.e., no inverse exists). A = 0 -1/2 1/2 4. Let A = -1 -1 (a) Compute A- if it exists. What is the rank of A. -(1/2)x2 + (1/2)x3 = (b) Use part (a) to solve the system = 1. 5. Let a (a) Check whether al, a', a" and a are linearly independent. (b) Find a maximally linearly independent subset of {al, a', a3, a*}. 6. Let A = 0 1 . Find 2 x 2 matrix B such that (ABAY )-1 = A-, where I is the identity matrix