The set of values of K for which the system of equations $\begin{bmatrix}2 & 3 & 1\\4 & 5 & 0\\1 & K & 3\end{bmatrix} \begin{bmatrix}x\\ y \\z\end{bmatrix}=\begin{bmatrix}5 \\ 6 \\ 7 \end{bmatrix}$ gives a unique solution is :

$\begin{Bmatrix}\frac{5}{4}\end{Bmatrix}$ $\begin{Bmatrix}-\frac{5}{4},\frac{5}{4}\end{Bmatrix}$ $\begin{Bmatrix}\frac{11}{4}\end{Bmatrix}$ $R-\begin{Bmatrix}\frac{11}{4}\end{Bmatrix}$

$R-\begin{Bmatrix}\frac{11}{4}\end{Bmatrix}$