First slide

System of linear equations

Question

$x + y + z = 1$ , $x + 2 y + 2 z = 3$ , $x + 2 y + λ z = 4$ have no solution is

Easy

A

0
B

1
C

2
D

3

Solution

$|\begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 2 \\ 1 & 2 & λ \end{matrix}| = 0 \Rightarrow |\begin{matrix} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 1 & λ - 1 \end{matrix}| = 0$
$\Rightarrow λ - 1 - 1 = 0 \Rightarrow λ = 2$ .

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