Question: If the system of equations$x - ky - z = 0$, $kx - y - z = 0$ and $x + y - z = 0$ has a non zer...

Question

If the system of equations $x - ky - z = 0$ , $kx - y - z = 0$ and $x + y - z = 0$ has a non zero solution, then the possible value of k are .

Answer 1

For non-trivial solution $\Delta = 0$

⇒ $\left| \begin{matrix} 1 & - k & - 1 \\ k & - 1 & - 1 \\ 1 & 1 & - 1 \end{matrix} \right| = 0$ ⇒ $k = 1, - 1.$

Question: If the system of equations\(x - ky - z = 0\), \(kx - y - z = 0\) and \(x + y - z = 0\) has a non zer...