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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Is the set W = {(x, y, z) ∈ R3: 2x + y - z = 0} a subspace? Explain.
💡 Hint: Check the zero vector and the closure properties.
Question 2
Easy
What is a basis for W = { (x,y,z): x=0 }?
💡 Hint: You need to express other variables in terms of the free ones.
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
What is a necessary condition for a subset W to be a subspace of R3?
- It must include the zero vector.
- It must be closed under addition.
- It must meet both conditions.
💡 Hint: Think about the properties necessary for vector spaces.
Question 2
True or False: Every set of linearly independent vectors forms a basis.
- True
- False
💡 Hint: Remember the definition of a basis.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Determine if the set W = {(x, y, z) ∈ R3: 3x - y + 4z = 5} can be a subspace.
💡 Hint: Check the zero vector first.
Question 2
Find a basis for the span of vectors {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and determine its dimension.
💡 Hint: Use row reduction to assess linear independence.
Challenge and get performance evaluation