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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 \(\mathbb{R}^{4}\) ?

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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?
by ♦ Diamond (89,175 points) | 192 views

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