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DETERMINANTS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDETERMINANTS1 Mark
Question
Evaluate $\begin{bmatrix}5&4&3\\3&4&1\\5&6&1\end{bmatrix}$is:
  1. 4
  2. -24
  3. -8
  4. 8
✓

Answer

  1. -8
Solution:
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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