37. A linear equation system Ax = b consists of m linear equations with n variables. Which of the following statements is correct?(A) We can apply elementary column operations to solve this linear equation system.(B) If A and B matrices are similar, then Ax=b and Bx=b have the same solution set.(C) If this linear equation system has solutions, the solutions form a subspace.(D) If m ≠ n and rank( A ) = m, then there exist infinite solutions.(E) If m ≠ n, we can use "Cramer's rule" to find its solution.

39. Which of the following statements is true?(A) Let S = {v₁, v₂, ..., vk} be a set of vectors in Rⁿ. Let A ∈ Mmxn(R). If S is linearly independent, then S' = {Av₁, Av₂, ..., Avk} is also linearly independent(B) Let S be a set of vectors in a finite-dimensional vector space V. Then, span(S) is the intersection of all subspaces of V that contains S(C) Assume that S = {v₁, v₂, ..., vn} is a subset of a vector space V. If S is linearly dependent, then there exists a proper subset of S that is a basis for V(D) The basis of any vector space is unique(E) Assume that S = {v₁, v₂, ..., vn} is a subset of a vector space V. If S is linearly independent, then there exists a proper subset of S that is a basis for V

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