Let $A=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 1\\ 0& -2& 4\end{array}\right]$ and $I=\left[\begin{array}{lll}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$, then

The system of equations
$x-y\cos \theta +z\cos 2\theta =0$

$-x\cos \theta +y-z\cos \theta =0$

$x\cos 2\theta -y\cos \theta +z=0$
has non-trivial solution for $\theta$ equals

Let $A=a_{ij}$ be a matrix of order $3\times 3$ where

$$\begin{gathered} a_{ij}=\left\{\begin{array}{l}x, \mathrm{if} i=j,x\in R \\ 1, \mathrm{if} \left|i-j\right|=1\\ 0, \mathrm{otherwise}\end{array}\right. \end{gathered}$$ 

then which of the following statement(s) is/are true?