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math125-lecture 4.3

# math125-lecture 4.3 - Sec 4.3 Saturday 11:23 PM Let V be a...

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Let V be a vector space with operations and and and let W be a non-empty set of vectors of V. If W is a vector space with respect to the operations and in V, then W is called a subspace of V. Sec 4.3 Saturday, February 06, 2010 11:23 PM Section4dot3 Page 1

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Let V be a vector space with operations and and and let W be a non-empty set of vectors of V. If W is a vector space with respect to the operations and in V, then W is called a subspace of V. A subspace can be thought of as a vector space W that is a part of a larger vector space V 4.3.1 Saturday, February 06, 2010 11:23 PM Section4dot3 Page 2
Let V be a vector space with operations and and and let W be a non-empty set of vectors of V. If W is a vector space with respect to the operations and in V, then W is called a subspace of V. A subspace can be thought of as a vector space W that is a part of a larger vector space V The elements in W are already vectors since they come from the known vector space V. And W inherits the vector space operations and from V. As a result, to check whether a set W is a vector space, it suffices to check only the closure properties. 4.3.2 Saturday, February 06, 2010 11:23 PM Section4dot3 Page 3

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Let V be a vector space with operations and and and let W be a non-empty set of vectors of V. If W is a vector space with respect to the operations and in V, then W is called a subspace of V. A subspace can be thought of as a vector space W that is a part of a larger vector space V The elements in W are already vectors since they come from the known vector space V. And W inherits the vector space operations and from V. As a result, to check whether a set W is a vector space, it suffices to check only the closure properties. If W is closed under and , W inherits the algebraic and inverse properties of V, so all other 8 properties of a vector space are satisfied. 4.3.3 Saturday, February 06, 2010 11:23 PM Section4dot3 Page 4