First slide

System of linear equations

Question

The system of equations $x + y + z = 0,$ $2 x + 3 y + z = 0$
and $x + 2 y = 0$ has

Easy

A

a unique solution; $x = 0, y = 0, z = 0$
B

infinite solutions
C

no solution
D

finite number of non-zero solutions

Solution

The given system of equations are
      $x + y + z = 0,$

      $2 x + 3 y + z = 0$

and $x + 2 y = 0$

Here, $| \begin{matrix} 1 & 1 & 1 \\ 2 & 3 & 1 \\ 1 & 2 & 0 \end{matrix} | = 1 (0 - 2) - 1 (0 - 1) + 1 (4 - 3)$

                               $= - 2 + 1 + 1 = 0$

$∴$ System has infinite solutions.

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