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…

Dedra L. Welch
Software Engineer | IT Architect | Web Developer

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…

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, .…

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…

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…

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…