The value of lambda for which the system of | vedclass

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Question

(d) The coefficient determinant $D = \left| {\,\begin{array}{*{20}{c}}2&{ - 1}&{ - 1}\1&{ - 2}&1\1&1&\lambda \end{array}\,}

Vedclass · Accepted Answer

$-2$

Vedclass · Answer

(d) The coefficient determinant $D = \left| {\,\begin{array}{*{20}{c}}2&{ - 1}&{ - 1}\1&{ - 2}&1\1&1&\lambda \end{array}\,} ight|$

= $3\lambda - 6$

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.

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

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