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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
Value of $k,$ for which $A=\left[\begin{array}{cc}k & 8 \\ 4 & 2 k\end{array}\right]$ is a singular matrix is
  • ✓
    $4$
  • B
    $-4$
  • C
    $\pm 4$
  • D
    $0$
✓

Answer

Correct option: A.
$4$
$\because A$ is a singular matrix.
$\therefore|A|=0 $
$\Rightarrow\left|\begin{array}{cc} k & 8 \\ 4 & 2 k \end{array}\right| =0 $
$\Rightarrow 2 k^2-32=0 $
$\Rightarrow k^2=16 $
$\Rightarrow k= \pm 4$

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