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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?
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