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Parkland College MAT 220: 4.2 Vector Spaces (Lecture Notes)

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Uploaded on: October 10, 2025
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parkland college mat 220 42 vector spaces

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4.2
Vector Spaces

,Definition of a Vector Space

, Definition of a Vector Space (1 of 6)
Definition of a Vector Space
Let V be a set on which two operations (vector addition
and scalar multiplication) are defined. If the listed
axioms are satisfied for every u, v, and w in V and every
scalar (real number) c and d, then V is a vector space.

Addition:
1. u + v is in V. Closure under addition
2. u + v = v + u Commutative property
3. u + (v + w) = (u + v) + w Associative property

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Parkland College MAT 220: 4.2 Vector Spaces (Lecture Notes)

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