I have a system of equations to solve $Ax = b$, but the determinant of matrix $A$ is zero.
$$A=\begin{bmatrix}1&1&0&0\\0&0&1&1\\1&0&1&0\\0&1&0&1\end{bmatrix}$$
To me, none of the rows/columns of this matrix look dependent. I am wondering why the determinant of matrix $A$ is zero?
Also, how should I solve this system or estimate $x$?