24.16 - Worked Examples
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Practice Questions
Test your understanding with targeted questions
Is the set W = {(x, y, z) ∈ R3: 2x + y - z = 0} a subspace? Explain.
💡 Hint: Check the zero vector and the closure properties.
What is a basis for W = { (x,y,z): x=0 }?
💡 Hint: You need to express other variables in terms of the free ones.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a necessary condition for a subset W to be a subspace of R3?
💡 Hint: Think about the properties necessary for vector spaces.
True or False: Every set of linearly independent vectors forms a basis.
💡 Hint: Remember the definition of a basis.
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Challenge Problems
Push your limits with advanced challenges
Determine if the set W = {(x, y, z) ∈ R3: 3x - y + 4z = 5} can be a subspace.
💡 Hint: Check the zero vector first.
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.
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Reference links
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