# For what values k is the system consistent?

Let $T : \mathbb{R} ^{2} \rightarrow \mathbb{R} ^{3}$ be a linear representation with a standard matrix $A = \begin{bmatrix} 1 & 2 & 3 \\ -2 & -4 & -k \end{bmatrix}$
where k is a number that we can vary. (Note that it is not an extended matrix).

a) For what values k is the system $Ax = \begin{bmatrix}-17\\34\end{bmatrix}$ consistent?

b) For what values k is the system $Ax = \begin{bmatrix}1\\34\end{bmatrix}$ consistent?

c) For what values k is the linear representation T onto?

d) For what values k is the linear representation T one-to-one?