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DETERMINANTS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDETERMINANTS1 Mark
Question
Choose the correct answer from given four options in each of the Exercise:
If $\text{f(x)}==\begin{vmatrix}0&\text{x}-\text{a}&\text{x}-\text{b} \\\text{x}+\text{a} &0&\text{x}-\text{c}\\\text{x}+\text{b}&\text{x}+\text{c}&0\end{vmatrix},$ then:
  1. f(a) = 0
  2. f(b) = 0
  3. f(0) = 0
  4. f(1) = 0
✓

Answer

  1. f(0) = 0

Solution:

$\text{f(x)}=\begin{vmatrix}0&\text{x}-\text{a}&\text{x}-\text{b} \\\text{x}+\text{a} &0&\text{x}-\text{c}\\\text{x}+\text{b}&\text{x}+\text{c}&0\end{vmatrix}$

$\Rightarrow\ \text{f}(0)=\begin{vmatrix}0&-\text{a}&-\text{b}\\\text{a}&0&-\text{c}\\\text{b}&\text{c}&0\end{vmatrix},$ Which is skew-symmetric determinant of order 3

Hence f(0) = 0.

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