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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 $\begin{vmatrix}2\text{x}&5\\8&\text{x}\end{vmatrix}=\begin{vmatrix}6&-2\\7&3\end{vmatrix},$ then value of x is:
  1. 3
  2. ±3
  3. ±6
  4. 6
✓

Answer

  1. ±6

Solution:

We have, $\begin{vmatrix}2\text{x}&5\\8&\text{x}\end{vmatrix}=\begin{vmatrix}6&-2\\7&3\end{vmatrix}$

$\Rightarrow\ 2\text{x}^2-40=18+17$

$\Rightarrow\ 2\text{x}^2=32+40$

$\Rightarrow\ \text{x}^2=\frac{72}{2}=36$

$\Rightarrow\ \text{x}^2=36$

$\Rightarrow\ \text{x}=\pm6$

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