First slide

Applications of determinant

Question

If $A = [\begin{array}{cc} 4 & x + 2 \\ 2 x - 3 & x + 1 \end{array}]$ is an invertible matrix, then x cannot take value

Moderate

A

-1
B

2
C

3
D

none of these

Solution

$| A | \neq 0 \Rightarrow 4 (x + 1) - (2 x - 3) (x + 2) \neq 0$
$\begin{array}{l} \Rightarrow 2 x^{2} - 3 x - 10 \neq 0 \\ \Rightarrow x \neq \frac{3 \pm \sqrt{89}}{4} \end{array}$

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