← MATH 01210 · Linear Algebra
MATH 01210 · Vector spaces
Basis & dimension
Definition
A basis of V is a linearly independent spanning set. Dimension dim V is the number of vectors in any basis (well-defined).
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Standard basis of Rⁿ: e₁,…,eₙ. Coordinate vectors relative to a basis B.
Any independent set of size dim V is a basis; any spanning set of that size is a basis.
Extend independent sets to bases; thin spanning sets down to bases.
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Attempt each problem first, then open the worked solution.
1.Find a basis for the plane x+y+z=0 in R³.