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4 cards from this section. Quick, good the night before a test.
What is the dimension of ℝ³?
Think about how many directions you can move in 3D space.
Is a vector space with a basis containing 5 vectors finite-dimensional?
Consider the definition of finite-dimensional spaces.
What is the dimension of the vector space ℝ⁵?
Recall how many independent vectors are required to describe this space.
True or False: A vector space can have only one finite basis.
Think about the nature of linear independence.
Show that the set of functions {1, x, x^2, ..., x^n} is a basis for the space of polynomials of degree ≤ n.
Explore how polynomial degrees restrict combinations.
Discuss why the dimension of the vector space of all sequences of real numbers is infinite.
Think about the nature of sequences and how they can continue indefinitely.
5 more questions in this section. Enroll free to practise them all.
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