First slide

System of linear equations

Question

The system of equations $x + y + z = 6, x + 2 y + 3 z = 10$ $, x + 2 y + λ z = k$ is inconsistent if $λ = ...., k \neq ....$

Moderate

A

3, 7
B

3, 10
C

7, 10
D

10, 3

Solution

Augment Matrix $[A D]$ $= [\begin{matrix} 1 & 1 & 1 & 6 \\ 1 & 2 & 3 & 10 \\ 1 & 2 & λ & k \end{matrix}]$ Apply: $R_{2} \to R_{2} - R_{1};$ $R_{3} \to R_{3} - R_{1}$
$~ [\begin{matrix} 1 & 1 & 1 & 6 \\ 0 & 1 & 2 & 4 \\ 0 & 1 & λ - 1 & k - 6 \end{matrix}]$ Apply : $R_{3} \to R_{3} - R_{2}$
$~ [\begin{matrix} 1 & 1 & 1 & 6 \\ 0 & 1 & 2 & 4 \\ 0 & 0 & λ - 3 & k - 10 \end{matrix}]$
The system is inconsistent, if $λ - 3 = 0, k - 10 \neq 0$
$\Rightarrow λ = 3, k \neq 10$

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