First slide

Applications of determinant

Question

If the matrix $[\begin{matrix} α & - 2 & 4 \\ 1 & - 3 & 2 \\ 4 & - 2 & 1 \end{matrix}]$ is non singular then $α \in$

Moderate

A

$R$
B

$R - {- 22}$
C

$R - {- 24}$
D

$R {- 26}$

Solution

$\begin{array}{l} |\begin{array}{lll} α & - 2 & 4 \\ 1 & - 3 & 2 \\ 4 & - 2 & 1 \end{array}| \neq 0 \\ \Rightarrow α (- 3 + 4) + 2 (1 - 8) + 4 (- 2 + 12) \neq 0 \end{array}$
$\begin{array}{l} α - 14 + 40 \neq 0 \\ α \neq - 26 \\ α \in R - {- 26} \end{array}$

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