by Seth Grief-Albert

Axioms

Theorems

Vector Subspaces

Weird Vector Space [W]

Span

The set of all linear combinations.

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$$ c_1v_1+c_2v_2+c_3v_3 $$

A span is a vector subspace. Vector subspaces are closed under vector addition and scalar multiplication.

Vector subspaces are closed under vector addition and scalar multiplication.

Any linear combination of elements in a vector space V will also be in the vector space.

Test

Coplanar

Linear Dependance

Redundancy

Non-zero scalar multiples of the vectors produce the zero-vector.

Although parallel vectors are dependent in R2, not all dependent vectors are parallel.