Consider the system of linear equations: x_1+3x_2+x_3+x_4=3…
Consider the system of linear equations: x_1+3x_2+x_3+x_4=3 2x_1-2x_2+ x_3+2x_4=8 3x_1+ x_2+2x_3 -x_4=-1. I. (a) Write the corresponding augmented matrix. (b) Do suitable row operations so that first column is all zero except for the entry in the first row. (3 points each). II. (a) Complete computing an echelon form for the above matrix. (8 points) (b) Find all possible solutions . (4 points) (c) How many solutions are there? Which are the basic variables and which are the free variables, if any? (2 points) III. Given the matrix A= , find A^{-1}. (10 points)