First slide

System of linear equations

Question

The system of equations $x + y + z = 1$ , $3 x + 6 y + z = 8$ , $α x + 2 y + 3 z = - 1$ has a unique solution for

Easy

A

$α \neq 0$
B

All real $α$
C

All integral $α$
D

All rational $α$

Solution

For a unique solution, $|\begin{matrix} 1 & 1 & 1 \\ 3 & 6 & 1 \\ α & 2 & 3 \end{matrix}| \neq 0$ ,
i.e., $α \neq \frac{13}{5}$ .

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