Question 1. Consider the augmented matrix of a linear system: T = 1 k ko1 1 11 -2 (a) Write the system of linear equations corresponding to the given augmented matrix. (b) Find a row echelon form of the given matrix. (c) (i) For what value(s) of k does the system have an infinite number of solutions? Give rea- soning. (11) For what value(s) of k is the system inconsistent? Give reasoning. (11) For what value(s) of k does the system have a unique solution? Give reasoning. (d) Find vectors u, v R? such that the solution set of the equation x +y z = 0 can be written as {su+tv|s,t R}