23.3 - Definition of Linear Independence
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Practice Questions
Test your understanding with targeted questions
Are the vectors [1, 0] and [0, 1] in R² linearly independent?
💡 Hint: Consider their geometric representation.
Determine if the vectors [1, 1] and [1, 2] are linearly independent.
💡 Hint: Look for a solution for coefficients that results in zero.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does it mean for a set of vectors to be linearly independent?
💡 Hint: Recall the definition given in class.
Is the set containing the zero vector linearly dependent?
💡 Hint: Consider the implications of the zero vector.
1 more question available
Challenge Problems
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Prove that the vectors (1, 1, 1), (2, 2, 2), (3, 3, 3) are linearly dependent by showing how one vector is a linear combination of the others.
💡 Hint: Set up the equation and solve using coefficient comparison.
Given vectors (1, 0) and (a, b) in R², find conditions on a and b for independence.
💡 Hint: Use the determinant condition for independence.
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