First slide

System of linear equations

Question

The value of $k$ for which the system of equations $x + k y + 3 z = 0$ , $3 x + k y - 2 z = 0$ and $2 x + 3 y - 4 z = 0$ has a non trivial solution is

Easy

A

33
B

$\frac{2}{33}$
C

$\frac{3}{2}$
D

None of these

Solution

The given system of equations have a non-trivial solution only if
$|\begin{matrix} 1 & k & 3 \\ 3 & k & - 2 \\ 2 & 3 & - 4 \end{matrix}| = 0$
i.e., if $- 4 k + 6 - k (- 12 + 4) + 3 (9 - 2 k) = 0$
i.e., if $- 4 k + 6 + 8 k + 27 - 6 k = 0$
i.e., if $- 2 k = - 33$ i.e., if $k = \frac{33}{2}$ .

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App