- Home
- Standard 12
- Mathematics
3 and 4 .Determinants and Matrices
medium
The value of $\lambda $ for which the system of equations $2x - y - z = 12,$ $x - 2y + z = - 4,$ $x + y + \lambda z = 4$ has no solution is
A
$3$
B
$-3$
C
$2$
D
$-2$
(IIT-2004)
Solution
(d) The coefficient determinant $D = \left| {\,\begin{array}{*{20}{c}}2&{ – 1}&{ – 1}\\1&{ – 2}&1\\1&1&\lambda \end{array}\,} \right|$
= $3\lambda – 6$
For no solution, the necessary condition is $D = 0$
i.e., $ – 3\lambda – 6 = 0 \Rightarrow \lambda = – 2$
It can be seen that for $\lambda = – 2,$ there is no solution for the given system or equations.
Standard 12
Mathematics
