Let U and V be finite-dimensional vector spaces. (a) Find a formula for dim(U X V) in terms of dim U and dim V. (b) If W is a subspace of V, show that dim ∆ = dim W, where ∆= {(w, w) : w is in W}
Let U and V be finite-dimensional vector spaces. (a) Find a formula for dim(U X V) in terms of dim U and dim V. (b) If W is a subspace of V, show that dim ∆ = dim W, where ∆= {(w, w) : w is in W}
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 43EQ
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Let U and V be finite-dimensional
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