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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
If the matrix $\left[ {\begin{array}{*{20}{c}}0&1&{ - 2}\\{ - 1}&0&3\\\lambda &{ - 3}&0\end{array}} \right]$ is singular, then $\lambda $=
  • A
    $-2$
  • B
    $-1$
  • C
    $1$
  • ✓
    $2$
✓

Answer

Correct option: D.
$2$
d
(d) The matrix $A = \left[ {\begin{array}{*{20}{c}}{\,\,0}&{\,\,1}&{ - 2}\\{ - 1}&{\,\,0}&{\,\,3}\\{\,\,\lambda }&{ - 3}&{\,\,0}\end{array}} \right]$ is singular

 $|A|$ = 0 ==> $0 - 1( - 3\lambda ) + ( - 2)(3) = 0$

$ \Rightarrow 3\lambda - 6 = 0 \Rightarrow \lambda = 2$.

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