First slide

System of linear equations

Question

The system of linear equations $x + y + z = 2$ , $2 x + y - z = 3$ , $3 x + 2 y + k z = 4$ has a unique solution if

Easy

A

$k \neq 0$
B

$- 1 < k < 1$
C

$- 2 < k < 2$
D

$k = 0$

Solution

The given system has a unique solution if
$| \begin{matrix} 1 & 1 & 1 \\ 2 & 1 & - 1 \\ 3 & 2 & k \end{matrix} | \neq 0$

Operate $R_{1} \to R_{1} + R_{2} - R_{3}$

i.e., if $- k (4 - 3) \neq 0$

i.e., $k \neq 0$ .

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