If an n times n matrix has n distinct eigenvalues, then its columns form a basis

Question

If an n times n matrix has n distinct eigenvalues, then its columns form a basis for R^n Let V be a 4-dimensional subspace of R^5 Every set of five vectors in V is linearly dependent. Let V be a 4-dimensional subspace of R^5 Every set of four vectors in V spans V. There is a 3-plane and a 2-plane in R^5 whose intersection is a line. Let V be a 3-dimensional subspace of R^5. There is a basis for R^5 consisting of 3 vectors in V and 2 vectors not in V. If V is a subspace of R^n, then (V^ub tack) = V.

Explanation / Answer

32. The statement is True.

33. The statement is True.

34. The statement is False.

35. The statement is False.

36. The statement is True.

37. The statement is True.

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