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

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