23.5 - Algebraic Criterion for Linear Independence
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Practice Questions
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Check if the vectors [1, 2], [2, 4] are linearly independent.
💡 Hint: Look for scalar multiples.
Are the vectors [1, 1] and [2, 2] independent?
💡 Hint: Can you express one in terms of the other?
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What defines linear independence?
💡 Hint: Think about the solution types.
True or False: A homogeneous system can have non-trivial solutions.
💡 Hint: Recall the definitions of trivial and non-trivial solutions.
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Challenge Problems
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Consider the vectors v_1 = [1, 2, 1], v_2 = [2, 4, 2], and v_3 = [4, 8, 4]. Show that these vectors are linearly dependent.
💡 Hint: Try row-reduction to explore relationships.
For the vectors v_1 = [1, 2, 3] and v_2 = [1, a, 3], determine the value(s) of 'a' for which they are independent.
💡 Hint: Set up your system and check the determinant.
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