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Joint Entrance Examination
Mathematics
Matrices and Determinants
Question 355
Question 355 of 472
Medium
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 a non-trivial solutions :
A
is an empty set
B
contains more than two elements
C
is a singleton
D
contains exactly two elements
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Official solution
\[\left| {
(
λ
−
1
2
2
1
2
−
λ
1
1
1
1
)
\begin{pmatrix} {\lambda - 1} & 2 & 2 \\ 1 & {2 - \lambda } & 1 \\ 1 & 1 & 1 \\ \end{pmatrix}
λ
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1
1
1
2
2
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λ
1
2
1
1
} \right| = 0\] \[ \Rightarrow {\left( {\lambda - 1} \right)^3} = 0 \Rightarrow \lambda = 1\]
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