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3 cards from this section. Quick, good the night before a test.
Define a vector space.
Think about the operations you can perform within it.
What is a basis of a vector space?
Consider the relationship between spanning and independence.
What is a vector space?
Remember the definition.
Is every basis a linearly independent set?
Consider the definition of basis.
Consider the set of vectors A = {(1,2), (2,4), (3,6)}. Prove if A is linearly independent or dependent.
Use the properties of scaling factors.
In a space R^4, you need to determine if the set { (1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1), (1,1,1,1) } is independent.
Consider the dimension relation.
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