Question

The set of values of k for which the system of equations x + y + z = 2, 2x + y - z = 3, 3x +2 y + kz = 4 has a unique solution, is _________.

Answer 1

The system of equations x + y + z = 2, 2x + y − z = 3 and 3x + 2y + kz = 4 has a unique solution.

$\therefore ∆=\left|\begin{array}{ccc}1& 1& 1\\ 2& 1& -1\\ 3& 2& k\end{array}\right|\ne 0$

$\Rightarrow 1\left(k+2\right)-1\left(2k+3\right)+1\left(4-3\right)\ne 0$

$\Rightarrow k+2-2k-3+1\ne 0$

$\Rightarrow k\ne 0$

Thus, the set of values of k for which the given system of equations has a unique solution is R − {0}.

The set of values of k for which the system of equations x + y + z = 2, 2x + y − z = 3, 3x + 2y + kz = 4 has a unique solution, is __R − {0}__.