. (a) Suppose W₁ and W₂ are subspaces in a vector space V and that V = W₁ + W₂. Prove that V = W₁ W₂ if and only if any vector v EV can be represented uniquely as v = v₁ + v2 where V₁ € W₁, V2 E W₂. = (b) Suppose W₁ and W₂ are subspaces in a vector space V, and such that V basis of W₁ and 32 is a basis of W2 prove that 3₁ U 32 is a basis of V. W₁ W₂. If B₁ is a
. (a) Suppose W₁ and W₂ are subspaces in a vector space V and that V = W₁ + W₂. Prove that V = W₁ W₂ if and only if any vector v EV can be represented uniquely as v = v₁ + v2 where V₁ € W₁, V2 E W₂. = (b) Suppose W₁ and W₂ are subspaces in a vector space V, and such that V basis of W₁ and 32 is a basis of W2 prove that 3₁ U 32 is a basis of V. W₁ W₂. If B₁ is a
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 21EQ
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