Practice Subspaces (26.3) - Vector Spaces - Mathematics (Civil Engineering -1)
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Subspaces

Practice - Subspaces

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What are the three conditions for a subset to be a subspace?

💡 Hint: Think about the defining properties of a vector space.

Question 2 Easy

Is the set of vectors { (1,0), (0,1), (1,1) } a subspace of ℝ²?

💡 Hint: Verify if zero vector is included and if adding two members gives another member.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is a requirement for a subset W to be a subspace of V?

It must contain at least two vectors
It must be closed under vector addition
It must not include the zero vector

💡 Hint: Think of the operations allowed within the vector space.

Question 2

True or False: All lines in ℝ² are subspaces.

True
False

💡 Hint: Recall the specific properties of subspaces you've learned.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove that the span of any set of vectors is a subspace.

💡 Hint: Start by considering what happens when you combine vectors in the span.

Challenge 2 Hard

Find two vectors in ℝ² that form a line through the origin and demonstrate the closure properties.

💡 Hint: Visualize this on a graph for clarity.

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