Determine the values of h such that the matrix is

Determine the values of h such that the matrix is the augmented matrix of a consistent linear system.
$\begin{bmatrix}1&h&5\\-2&6&-15\end{bmatrix}$

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Witionsion
The augmented matrix is given as
$\begin{bmatrix}1&h&5\\-2&6&-15\end{bmatrix}$
Reduce this augmented matrix to echelon form
Consider
$\begin{bmatrix}1&h&5\\-2&6&-15\end{bmatrix}$
$$\displaystyle{R}_{{2}}\to{R}_{{2}}+{2}{R}_{{1}}$$
$\begin{bmatrix}1&h&5\\0&6+2h&-5\end{bmatrix}$
This system is inconsistent if and only if
$$\displaystyle{6}+{2}{h}={0}$$
$$\displaystyle{2}{h}=-{6}$$
$$\displaystyle{h}=-{3}$$
Hence this system is consistent if and only if $$\displaystyle{h}\ne-{3}$$
Therefore option (A) is correct.