Let U and W be subspaces of a finite-dimensional vector space V. Prove Grassmanns
Chapter 6, Problem 6.2.42(choose chapter or problem)
Let U and W be subspaces of a finite-dimensional vector space V. Prove Grassmanns Identity: dim(U W) dimU dimW dim(U W) [Hint: The subspace U W is defined in Exercise 48of Section 6.1. Let B {v1,..., vk} be a basis forU W. Extend B to a basis C of U and a basis D of W.Prove that C D is a basis for U W.]
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