Determine if the following subset of $M_{2\times 2}$ is linearly independent: $$U = \left\lbrace\begin {bmatrix} 1&1 \\\\ 0&1 \ \end{bmatrix}, \begin {bmatrix} 1&0 \\\\ 1&1 \ \end{bmatrix}, \begin {bmatrix} 1&1 \\\\ 1&1 \ \end{bmatrix} \right\rbrace$$
I am approaching the problem with: $$ c_1 \begin {bmatrix} 1&1 \\\\ 0&1 \ \end{bmatrix} + c_2 \begin {bmatrix} 1&0 \\\\ 1&1 \ \end{bmatrix} + c_3 \begin {bmatrix} 1&1 \\\\ 1&1 \ \end{bmatrix} = 0$$ from the above I get: $$c_1+c_2+c_3=0 \\ c_1 + c_3=0 \\ c_2+c_3=0 \\ c_1+c_2+c_3=0$$ but when I solve it, I end up with an inconsistent system. Doesn't this mean the system is neither LI or LD? Or did I mess up somewhere.