Find the value of x, if \[\begin{vmatrix}x + 1 & x - 1 \\ x - 3 & x + 2\end{vmatrix} = \begin{vmatrix}4 & - 1 \\ 1 & 3\end{vmatrix}\]

\[\text{ Given }: \begin{vmatrix}x + 1 & x - 1 \\ x - 3 & x + 2\end{vmatrix} = \begin{vmatrix}4 & - 1 \\ 1 & 3\end{vmatrix}\] \[ \Rightarrow \left( x + 1 \right)\left( x + 2 \right) - \left( x - 3 \right)\left( x - 1 \right) = 12 + 1\] \[ \Rightarrow x^2 + 3x + 2 - x^2 + 4x - 3 = 13\] \[ \Rightarrow 7x - 1 = 13\] \[ \Rightarrow 7x = 14\] \[ \Rightarrow x = 2\]

Find the Value of X, If ∣ ∣ ∣ X + 1 X − 1 X − 3 X + 2 ∣ ∣ ∣ = ∣ ∣ ∣ 4 − 1 1 3 ∣ ∣ ∣ - Mathematics

Question

Find the value of x, if

$| \begin{matrix} x + 1 & x - 1 \\ x - 3 & x + 2 \end{matrix} | = | \begin{matrix} 4 & - 1 \\ 1 & 3 \end{matrix} |$

Solution

$Given : | \begin{matrix} x + 1 & x - 1 \\ x - 3 & x + 2 \end{matrix} | = | \begin{matrix} 4 & - 1 \\ 1 & 3 \end{matrix} |$
$\Rightarrow (x + 1) (x + 2) - (x - 3) (x - 1) = 12 + 1$
$\Rightarrow x^{2} + 3 x + 2 - x^{2} + 4 x - 3 = 13$
$\Rightarrow 7 x - 1 = 13$
$\Rightarrow 7 x = 14$
$\Rightarrow x = 2$

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Applications of Determinants and Matrices

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Q 10.5 Q 10.4 Q 10.6

Chapter 6: Determinants - Exercise 6.1 [Page 10]

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Chapter 6 Determinants
Exercise 6.1 | Q 10.5 | Page 10

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