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Proofs For Linear Algebra Problem 3: Let V be a finite dimensional vector space and let S be a spanning set for V . Prove that a subset B of S can be chosen which is a basis for V . (Hint: Let n = |S| − dim V ≥ 0 and prove by induction on n)

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Proofs For Linear Algebra

Problem 3: Let V be a finite dimensional vector space and let S be a spanning set for V . Prove that a subset B of S can be chosen which is a basis for V . (Hint: Let n = |S| − dim V ≥ 0 and prove by induction on n)

Problem 4: Prove that if A and B are similar matrices, then A and B have the same eigenvalues.

Problem 5: Prove that a linear transformation L is injective if and only if ker(L) is the trivial vector space

 
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