21.8.3 - Basis and Dimension
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Practice Questions
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What is a basis in vector space?
💡 Hint: Think about how vectors can represent points in space.
How is the dimension of a vector space determined?
💡 Hint: Consider how many directions can be formed by the basis vectors.
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Interactive Quizzes
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What is a basis in linear algebra?
💡 Hint: Remember the definition of linear combinations.
Dimension refers to:
💡 Hint: Think of how many directions the basis can point.
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Challenge Problems
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Determine if the vectors (3,1,2), (2,0,0), and (0,4,1) are linearly independent. What is the dimension of their span?
💡 Hint: Try arranging the vectors into a matrix to examine their independence.
Given a vector space of dimension 5, what are possible bases for it, and how would you verify their independence?
💡 Hint: Consider the geometric interpretation of vector directions.
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