If $2 a x - 2 y + 3 z = 0, x + a y + 2 z = 0, 2 x + a z = 0$ have a nontrivial solution, find the value of $a$

Open in App

Solution

$2 a x - 2 y + 3 z = 0, x + a y + 2 z = 0, 2 x + a z = 0$ have a nontrivial solution.
$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 2 a & - 2 & 3 1 & a & 2 2 & 0 & a \end{matrix} ∣ ∣ ∣ ∣ = 0$
$\Rightarrow 2 a (a^{2}) + 2 (a - 4) + 3 (- 2 a) = 0$
$\Rightarrow a^{3} - 2 a - 4 = 0$
$\Rightarrow (a - 2) (a^{2} + 2 a + 2) = 0$
$∴ a = 2$

Suggest Corrections

Similar questions

2 a x - 2 y + 3 z = 0, x + a y + 2 z = 0 and 2 x + a z = 0

a

x - y + z = 0, x + 2 y - z = 0, 2 x + y + 3 z = 0

k

x + k y + 3 z = 0, 3 x + k y - 2 z = 0, 2 x + 3 y - 4 z = 0

\frac{2 k}{11}

Join BYJU'S Learning Program