For which real numbers \(x\) do the vectors: \((x, 1,1,1),(1, x, 1,1),(1,1, x, 1),(1,1,1, x)\) not form a basis of \(\mathbb{R}^{4}\) ? For each of the values of \(x\) that you find, what is the dimension of the subspace of \(\mathbb{R}^{4}\) that they span?