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2 cards from this section. Quick, good the night before a test.
What is a basis in a vector space?
Think about the minimal number of vectors needed to describe all vectors in the space.
Give an example of a basis for R².
Consider the axes in a two-dimensional space.
What is a basis of a vector space?
Remember the properties that define a basis.
True or False: The vectors (1,2) and (1,2) can form a basis for R².
Consider if the vectors can be combined to give you the identity vector.
Find a basis for the vector space spanned by the vectors {(2,4), (-1,-2), (3,6)}.
Identify which vectors are linearly dependent.
Determine if the set {(1,1), (2,2), (3,4)} is a basis for R². Explain your reasoning.
Try expressing one vector as a combination of others.
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