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Examples of vector spaces

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The solutions to a homogeneous linear differential equation is a vector space.
The set of all polynomials is a vector space.
The set of all polynomials of degree at most n is a vector space.
The set of all sequences is a vector space.
The crazy vector space is a vector space.
The set containing only 0 is a vector space.
F^n is a vector space.
R^n is a vector space.
C^n is a vector space.
The set of all functions on a set is a vector space.
The solutions to a homogeneous system of linear equations is a vector space.
The set of m by n matrices is a vector space.
The row space of a matrix is a vector space
The column space of a matrix is a vector space
The null space of a matrix is a subspace of R^n (or C^n).
The left null space of a matrix is a subspace of R^m (or C^m).
The set of linear transformations between two vector spaces is a vector space.

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The solutions to a homogeneous linear differential equation is a vector space.

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The solutions to a homogeneous system of linear equations is a vector space.Close match
The solutions to a nonhomogeneous system are given by a particular solution plus the solutions to the homogeneous system.Close match
The set of linear transformations between two vector spaces is a vector space.Close match
Vector form of solutions to a consistent linear systemClose match
A homogeneous system has a nontrivial solution if and only if it has a free variable.Close match
A homogeneous system with more variables than equations has infinitely many solutions.Close match
The solutions of a homogeneous system are the pre-image (of 0) of a linear transformation.Close match
Definition of homogeneous linear system of equationsClose match
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Definition of nontrivial solution to a homogeneous linear system of equationsClose match
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A scalar multiple of a linear transformation is a linear transformationClose match
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The crazy vector space is a vector space.Close match
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The geometry of linear systemsRelated
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