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4 cards from this section. Quick, good the night before a test.
Define a vector space.
Think about the operations we perform on vectors.
What is a subspace?
What must the subset satisfy?
What is a vector space?
Think about what defines a vector space.
Is a subspace a vector space?
Recall what a subset must satisfy.
Given three vectors in R^3, determine if they form a basis. Show your calculations.
Use row reduction to check for independence.
You have a vector space of dimension 5. If you remove one vector that is part of the basis, what happens to the dimension? Explain your reasoning.
How do basis vectors relate to the definition of dimension?
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