Vector Spaces
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Basis and dimension
A linear combination of two vectors is defined as follows. If[Equation goes here - download the original to see it.]and[Equation goes here - download the original to see it.]are two vectors of the vector space V then any vector of the form[Equation goes here - download the original to see it.]where[Equation goes here - download the original to see it.]is called a linear combination of[Equation goes here - download the original to see it.]and[Equation goes here - download the original to see it.]. A linear combination of vectors[Equation goes here - download the original to see it.]takes the form [Equation goes here - download the original to see it.] where [Equation goes here - download the original to see it.] Example [Equation goes here - download the original to see it.] Solution [Equation goes here - download the original to see it.]
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Contents of
Vector Spaces
1 Vector Spaces
2 Linear polynomials
3 Complex numbers
4 Quadratic polynomials
5 Continuous Functions
6 Infinite sequences
7 Vector space axioms
8 Properties of vector spaces
9 Subspaces of vector spaces
10 Basis and dimension
11 Span
12 Theorem (Vector spaces)
13 Vectors, dimension and bases
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