List of top Mathematics Questions on Systems of Linear Equations

The number of values of $k$ for which the following system of linear equations: \[ \begin{pmatrix} 4 & k & 2\\ k & 4 & 1\\ 2 & 2 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix} \] possess a non-zero solution, is _______

For a system \(AX = b\) of linear equations to have infinitely many solutions, which one of the following options must be true?