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?
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