First slide

System of linear equations

Question

The system of equations $x + 4 y - 2 z = 3, 3 x + y + 5 z = 7, 2 x + 3 y + z = 5$ has

Moderate

A

Infinite number of solutions
B

Unique solution
C

Trivial solution
D

No solution

Solution

Augmented matrix $= [\begin{matrix} 1 \\ 3 \\ 2 \end{matrix} \begin{matrix} 4 & - 2 & 3 \\ 1 & 5 & 7 \\ 3 & 1 & 5 \end{matrix}]$ apply: $\begin{array}{l} R_{2} \to R_{2} - 3 R_{1} \\ R_{3} \to R_{3} - 2 R_{1} \end{array}$
$~ [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix} \begin{matrix} 4 & - 2 & 3 \\ - 11 & 11 & - 2 \\ - 5 & 5 & - 1 \end{matrix}]$ apply: $R_{3} \to 11 R_{3} - 5 R_{1}$
$~ [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix} \begin{matrix} 4 & - 2 & 3 \\ - 11 & 11 & - 2 \\ 0 & 0 & 1 \end{matrix}]$
$∵$ $r a n k A = 2, r a n k [A B] = 3 \Rightarrow r a n k A \neq r a n k [A B]$
$∴$ The system is inconsistent, hence no solution.

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