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# There exists a real number such that the equation does not have any solutions in t and s. Find k.

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There exists a real number $$k$$ such that the equation $$\begin{pmatrix} -1 \\ -2 \end{pmatrix} + t \begin{pmatrix} \phantom -3 \\ -2 \end{pmatrix} = \begin{pmatrix} 5 \\ 0 \end{pmatrix} + s \begin{pmatrix} 4 \\ k \end{pmatrix}$$
does not have any solutions in t and s. Find k.

Feb 8, 2020