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4 cards from this section. Quick, good the night before a test.
Define vector space.
Remember the properties like closure and identity.
What is a subspace?
Think of it as a 'mini vector space.'
What is a defining property of a vector space?
Think about how operations are handled.
True or False: A subspace must contain the zero vector.
Consider the origins of vector spaces.
Prove that the set of all vectors of the form (a, 0) in R^2 is a subspace. Include a demonstration that it obeys all vector space rules.
Focus on adding two vectors and multiplying by different scalars.
Given four vectors in R^3, determine if they can form a basis based on their linear independence and span. Provide steps for your reasoning.
Determinants can also help in checking linear independence.
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