First slide

Elementary row operations (Transformation)

Question

The system of equations $2 x + y - z = 7$ , $x - 3 y + 2 z = 1$ , $x + 4 y - 3 z = 5$ is

Moderate

A

Consistant
B

Inconsistant
C

Unique solutions
D

None

Solution

$[A B] = [\begin{matrix} 2 & 1 & - 1 \\ 1 & - 3 & 2 \\ 1 & 4 & - 3 \end{matrix} \begin{matrix} 7 \\ 1 \\ 5 \end{matrix}] ~ [\begin{matrix} 2 & 1 & - 1 \\ 0 & - 7 & 5 \\ 0 & 7 & - 5 \end{matrix} \begin{matrix} 7 \\ - 5 \\ 3 \end{matrix}]$ $\begin{matrix} 2 R_{2} - R_{1} \\ 2 R_{3} - R_{1} \end{matrix}$ ~ $[\begin{matrix} 2 & 1 & - 1 \\ 0 & - 7 & 5 \\ 0 & 0 & 0 \end{matrix} \begin{matrix} 7 \\ - 5 \\ - 2 \end{matrix}]$ $R_{3} + R_{2}$
Rank (A) = 2, Rank of (AB) =3
Inconsistant

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