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DETERMINANTS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDETERMINANTS1 Mark
Question
If$\begin{bmatrix} \text{x} +1& \text{x} - 1\\ \text{x} - 3 & \text{x} + 2 \\ \end{bmatrix} = \begin{bmatrix} 4 & -1 \\ 1 &3 \\ \end{bmatrix}$, then write the value of x.
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Answer

Given $\begin{bmatrix} \text{x} +1& \text{x} - 1\\ \text{x} - 3 & \text{x} + 2 \\ \end{bmatrix} = \begin{bmatrix} 4 & -1 \\ 1 &3 \\ \end{bmatrix}$
$\Rightarrow(\text{x} + 1 ) (\text{x} + 2) - (\text{x} - 1 )(\text{x} - 3 ) = 12+ 1 $
$\Rightarrow\text{x}^{2} + 2 \text{x} + \text{x} + 2 - \text{x}^{2} + 3 \text{x} + \text{x} - 3 = 13$
$\Rightarrow7\text{x} - 1 = 13$
$\Rightarrow 7\text{x} = 14$
$\Rightarrow\text{x} = 2.$

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