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
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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…

A proof of the irrationality of just to try in WordPress Assume is rational. Then and such that where and are integers and is in lowest terms. is even is even is divisible by such that substitute for in the…