Math 2331 { Linear Algebra

Vector Spaces & SubspacesMath 2331 Linear Vector Spaces & SubspacesJiwen HeDepartment of Mathematics, University of jiwenhe/math2331 Jiwen He, University of HoustonMath 2331, Linear Algebra1 / Vector Spaces & SubspacesVector Spaces Subspaces Determining Vector Spaces & SubspacesVector Spaces: DefinitionVector Spaces: Examples2 2 matricesPolynomialsSubspaces: DefinitionSubspaces: ExamplesDetermining SubspacesJiwen He, University of HoustonMath 2331, Linear Algebra2 / Vector Spaces & SubspacesVector Spaces Subspaces Determining SubspacesVector SpacesMany concepts concerning vectors inRncan be extended to othermathematical can think of avector spacein general, as a collection ofobjects that behave as vectors do inRn. The objects of such a setare SpaceAvector spaceis a nonempty setVof objects, calledvectors, onwhich are defined two operations, calledadditionandmultiplication by scalars(real numbers), subject to the ten axiomsbelow.

Jiwen He, University of Houston Math 2331, Linear Algebra 10 / 21. 4.1 Vector Spaces & Subspaces Vector SpacesSubspacesDetermining Subspaces Subspaces: Example Example Let H = 8 <: 2 4 a 0 b 3 5: a and b are real 9 =;. Show that H is a subspace of R3. Solution: Verify properties a, b and c of the de nition of a

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