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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
The set of all values of $\lambda $ for which the system of linear equations $x - 2y - 2z = \lambda x$ ; $x + 2y + z = \lambda y$ ; $-x - y = \lambda z$ has non zero solutions.
  • ✓
    is a singleton
  • B
    contains exactly two elements
  • C
    is an empty set
  • D
    contains more than two elements
✓

Answer

Correct option: A.
is a singleton
a
$\left| {\begin{array}{*{20}{c}}
{\lambda  - 1}&2&2\\
1&{2 - \lambda }&1\\
1&1&1
\end{array}} \right| = 0$

$ \Rightarrow {\left( {\lambda  - 1} \right)^3} = 0 \Rightarrow \lambda  = 1$

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