Question:
The set of real values of a for which the matrix $A=\left[\begin{array}{ll}a & 2 \\ 2 & 4\end{array}\right]$ is non-singular is_________
Solution:
Given: The matrix $A=\left[\begin{array}{ll}a & 2 \\ 2 & 4\end{array}\right]$ is non-singular
$A$ is non-singular $\Rightarrow|A| \neq 0$
Thus,
$\left|\begin{array}{ll}a & 2 \\ 2 & 4\end{array}\right| \neq 0$
$\Rightarrow 4 a-4 \neq 0$
$\Rightarrow 4 a \neq 4$
$\Rightarrow a \neq 1$
$\Rightarrow a \in R-\{1\}$
Hence, the set of real values of a for which the matrix $A=\left[\begin{array}{ll}a & 2 \\ 2 & 4\end{array}\right]$ is non-singular is $R-\{1\}$