23.10 - Exercises
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Practice Questions
Test your understanding with targeted questions
Determine if the set of vectors { (1,0), (0,1) } is linearly independent.
💡 Hint: Consider their geometric representation.
Is the vector { (1,1), (1,1) } linearly independent?
💡 Hint: Look for redundancy in vectors.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
True or False: A set of vectors is linearly independent if at least one vector can be expressed as a combination of others.
💡 Hint: Recall the definitions of independence and dependence.
Which of the following sets of vectors are linearly dependent? {(1,0),(1,0)}, {(1,2),(2,4)}, or {(1,1),(1,-1)}?
💡 Hint: Look for vectors that can be expressed in terms of each other.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given the vectors {(1,2,3), (2,4,6), (3,6,9)}, demonstrate through matrix methods that they are dependent.
💡 Hint: Look at the ratios between the rows.
In R^3, provide a set of four vectors and argue whether they can be independent or dependent.
💡 Hint: Recall dimensional limits in linear algebra.
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