First slide

System of linear equations

Question

The system of linear equations $x + λ y - z = 0, λ x - y - z = 0, x + y - λ z = 0$
has a non-trivial solution for

Moderate

A

Infinitely many values of $λ$
B

exactly one values of $λ$
C

exactly ‘2’ values of $λ$
D

exactly ‘3’ values of $λ$

Solution

$T h e c o n d i t i o n f o r a h o m o g e n e o u s s y s t e m o f e q u a t i o n s t o h a v e a n o n - t r i v i a l s o l u t i o n i s Δ = 0$
$\Rightarrow$ $|\begin{array}{l} 1 λ - 1 \\ λ - 1 - 1 \\ 1 1 - λ \end{array}| = 0$
$\begin{array}{l} \Rightarrow (λ + 1) - λ (- λ^{2} + 1) - (λ + 1) = 0 \\ \Rightarrow λ (λ^{2} - 1) = 0 \\ \Rightarrow λ = 0, 1, - 1 \end{array}$

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