1. Matrix question

Hi there, I was asked the following question:

The matrix:
$\displaystyle \begin{bmatrix} 1 & 1 & 2 \\3 & 2 & -2\\2 & 1 & k \end{bmatrix}$$\displaystyle \begin{bmatrix} 4 \\1\\2\end{bmatrix}$
has no solutions.

Find the value of k.
I got k = -4 as that's when inconsistency occurs.

Could you give it a bash and tell me what you get for it please? I'm a little unsure of it.

Thanks a lot

2. It's not the matrix, but the system of equations $\displaystyle \begin{bmatrix} 1 & 1 & 2 \\3 & 2 & -2\\2 & 1 & k \end{bmatrix}\begin{bmatrix} x\\y\\z\end{bmatrix} = \begin{bmatrix} 4 \\1\\2\end{bmatrix}$, that has no solution when k = –4. But yes, k = –4 is when the inconsistency occurs.