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STD 12 - 3 and 4 . determinant and metrices — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3 and 4 . determinant and metrices4 Marks
MCQ
In order that the matrix $\left[ {\begin{array}{*{20}{c}}1&2&3\\4&5&6\\3&\lambda &5\end{array}} \right]$ be non-singular, $\lambda $ should not be equal to
  • A
    $1$
  • B
    $2$
  • C
    $3$
  • ✓
    $4$
✓

Answer

Correct option: D.
$4$
d
(d) Matrix $\left[ {\begin{array}{*{20}{c}}1&2&3\\4&5&6\\3&\lambda &5\end{array}} \right]$be non singular,

only if $\left| {\,\begin{array}{*{20}{c}}1&2&3\\4&5&6\\3&\lambda &5\end{array}\,} \right| \ne 0$

==> $\,1(25 - 6\lambda ) - 2(20 - 18) + 3(4\lambda - 15) \ne 0$

==> $25 - 6\lambda - 4 + 12\lambda - 45 \ne 0$

==> $6\lambda - 24 \ne 0$ ==> $\lambda \ne 4$.

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