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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Determine if the following vectors are linearly independent: [1, 2], [2, 3].
💡 Hint: Try forming a linear equation with both vectors.
Question 2
Easy
Are the vectors [1, 0] and [0, 1] linearly independent?
💡 Hint: Think about spanning a plane.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
A set of vectors is linearly independent if:
- At least one vector can be expressed as a linear combination of others
- The only solution to their linear combination equaling zero is non-trivial
- The only solution to their linear combination equaling zero is trivial
💡 Hint: Recall what a trivial solution is.
Question 2
If a set of vectors are collinear in R^2, are they linearly independent?
- True
- False
💡 Hint: Think about spanning a plane.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Show that the vectors [1, 0, 0], [0, 1, 0], [0, 0, 1] form a basis for R^3.
💡 Hint: Check for linear combinations.
Question 2
Given vectors in R^3, [x, 2x, 3x], under what conditions for 'x' are they dependent?
💡 Hint: Consider the implications of scalar multiples.
Challenge and get performance evaluation