For a Vandermonde Matrix (a) Explain why showing that det(A) 6= 0 is the same as showing that det(A^t) 6= 0, where A^t means the transpose of A. [This is a very short answer]. (b) Explain why showing that det(A^t) 6= 0 is the same as showing that A^t has no nonzero vector in the kernel. (c) if ~v = (c0, c1, . . . , cn−1) is a vector in the kernel of At, and ~v is not the zero vector, explain how this would give you a polynomial of degree ≤ n − 1 with more than n−1 roots, which would be a contradiction. [Hint: consider what At~v = 0 means.]

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For a Vandermonde Matrix (a) Explain why showing that det(A) 6= 0 is the same as showing that det(A^t) 6= 0, where A^t means the transpose of A. [This is a very short answer]. (b) Explain why showing that det(A^t) 6= 0 is the same as showing that A^t has no nonzero vector in the kernel. (c) if ~v = (c0, c1, . . . , cn−1) is a vector in the kernel of At, and ~v is not the zero vector, explain how this would give you a polynomial of degree ≤ n − 1 with more than n−1 roots, which would be a contradiction. [Hint: consider what At~v = 0 means.]

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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that 6 shouldn't be there, it should be (a) Explain why showing that det(A) cant equal 0 is the same as showing that det(A^t) cant equal 0, where A^t means the transpose of A. [This is a very short answer]. (b) Explain why showing that det(A^t) cant equal 0 is the same as showing that A^t has no nonzero vector in the kernel.

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