The Eckart-Young theorem states that the best rank-k approximation to matrix A in Frobenius norm is obtained by which of the following?

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Randomly selecting k columns of A and projecting the remaining columns onto their span.

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Keeping only the k largest singular values in Sigma and their corresponding columns in U and V: A_k = U_k * Sigma_k * V_k-transpose.

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Zeroing out the k smallest singular values and keeping the rest in a separate matrix.

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Performing Gram-Schmidt orthogonalization on k randomly chosen rows of A.

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