First slide

Introduction to Determinants

Question

The solutions of the equation $|\begin{matrix} x & 2 & - 1 \\ 2 & 5 & x \\ - 1 & 2 & x \end{matrix}| = 0$ are

Easy

A

$3, - 1$
B

$- 3, 1$
C

$3, 1$
D

$- 3, - 1$

Solution

$|\begin{matrix} x & 2 & - 1 \\ 2 & 5 & x \\ - 1 & 2 & x \end{matrix}| = 0 \Rightarrow x (5 x - 2 x) - 2 (2 x + x) - 1 (4 + 5) = 0$
$\Rightarrow 3 x^{2} - 6 x - 9 = 0, x^{2} - 2 x - 3 = 0, (x + 1) (x - 3) = 0 \Rightarrow x = - 1, 3$

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