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?

Solve the following expression: \[ \frac{x}{x - 1} \times \frac{x + 1}{x} \]

If the operation \(\ast\) is defined as \(a \ast b = 2a + b\), then \((2 \ast 3) \ast 4\) is:

Solve the system: \[ \begin{pmatrix} x \\ y \end{pmatrix} \quad \Rightarrow \quad \begin{pmatrix} 2x - 1 \\ 9 \end{pmatrix} \] Find the values of \(x\) and \(y\).