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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
Evaluate $\begin{bmatrix}5&4&3\\3&4&1\\5&6&1\end{bmatrix}$ is:
  • A
    $4$
  • B
    $-24$
  • ✓
    $-8$
  • D
    $8$
✓

Answer

Correct option: C.
$-8$
Expanding along the first row, we get
$\triangle=5\begin{bmatrix}4&1\\6&1\end{bmatrix}-4\begin{bmatrix}3&1\\5&1\end{bmatrix}+3\begin{bmatrix}3&4\\5&6\end{bmatrix}$
$=5(4-6)-4(3-5)+3(18-20)$
$=5(-2)-4(-2)+3(-2)$
$=-10+8-6$
$=-8.$

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