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Linear Algebra Done Right 2nd Edition – Chapter 1 Exercise 9

Chapter 1 Exercise 9. Prove that the union of two subspaces of V is a subspace of V if and only if one of the subspaces is contained in the other. Therefore, by 1 and 2, the union of two

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Linear Algebra Done Right 2nd Edition – Chapter 1 Exercise 8

Chapter 1 Exercise 8.Prove the intersection of any collection of subspaces of V is a subspace of V . Proof: Let be subspaces of . Then . Thus, (1) Therefore, . Suppose . Then . Since is a subspace, .

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Linear Algebra Done Right 2nd Edition – Chapter 1 Exercises 5(b), 5(c), 5(d), 6, 7

Chapter 1 5.(b)Determine if is a subspace of . Solution: Since . Thus is not a subspace of . 5.(c)Determine if is a subspace of . Solution: Since at least one of . Consider and . Both are in but

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Linear Algebra Done Right 2nd Edition – Chapter 1 Exercises 2, 3, 4, 5(a)

Chapter 1 2. Show that is a cube root of 1 (meaning that its cube equals 1). Solution: 3. Prove that for every . Solution: by proposition 1.6 by proposition 1.6 This is the alternate proof suggested in the solutions

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Linear Algebra Done Right 2nd Edition – Solutions to Selected Problems

Today, I’m starting a series of posts on my solutions to selected problems in the popular mathematics text Linear Algebra Done Right by Sheldon Axler. This is the second time I have worked through the exercises. The first time, I was

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