Chapter 1.2, Problem 50E

Matrix Representation In Exercises 49 and 50, assume that the matrix is the augmented matrix of a system of linear equations, and (a) determine the number of equations and the number of variables, and (b) find the value(s) of k such that the system is consistent. Then assume that the matrix is the coefficient matrix of a homogeneous system of linear equations, and repeat parts (a) and (b).

$A=\left[\begin{array}{ccc}2& -1& 3\\ -4& 2& k\\ 4& -2& 6\end{array}\right]$