First slide

System of linear equations

Question

The system of equations $- 2 x + y + k z = 1, 1 - 2 y + 3 z = 2, x + y - 2 z = 3$ is consistent if

Easy

A

$a + b + c = 0$
B

$a + b + c \leq 0$
C

$k \neq - 1$
D

$a + b + c \geq 0$

Solution

$\begin{array}{l} |\begin{matrix} - 2 & 1 & k \\ 1 & - 2 & 3 \\ 1 & 1 & - 2 \end{matrix}| \neq 0 \\ \Rightarrow - 2 [1] - [- 5] + k [3] \neq 0 \\ \Rightarrow - 2 + 5 + 3 k \neq 0 \\ \Rightarrow 3 k + 3 \neq 0 \Rightarrow k \neq - 1 \end{array}$

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