Question

If $\left[\begin{array}{ccc}1& a& 1\end{array}\right]\left[\begin{array}{c}2a\\ a\\ 2\end{array}\right]=\left[\begin{array}{c}1\end{array}\right]$, then the value of $a$ is

$\left(a\right)1\left(b\right)-1$
$\left(c\right)2\left(d\right)-2$

Answer 1

$\left[\begin{array}{ccc}1& a& 1\end{array}\right]\left[\begin{array}{c}2a\\ a\\ 2\end{array}\right]=\left[\begin{array}{c}1\end{array}\right]$
By matrix multiplication, we have
$2a+a^2+2=1$
$\Rightarrow a^2+2a+1=0$
$\Rightarrow (a+1{)}^2=0$
$\Rightarrow a=-1$

​​​​​​​Option $\left(b\right)$ is correct.