Practice Subspace - 24.3 | 24. Vector Space | Mathematics (Civil Engineering -1)
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Subspace

24.3 - Subspace

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Learning

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 both operations: addition and scalar multiplication.

Question 2 Easy

Give an example of a zero vector in R².

💡 Hint: What are the components that make a vector zero?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is a key requirement for a subset to be a subspace?

It must contain more than one vector
It must contain the zero vector
It must be infinite-dimensional

💡 Hint: Think about the foundational element shared by all vector spaces.

Question 2

True or False: Any linear combination of vectors in a subspace will result in a vector that is also in the subspace.

True
False

💡 Hint: Consider the definition of span.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given vectors (2, 3) and (4, 6) in R², determine if their span forms a subspace of R².

💡 Hint: Check if the vectors are linearly independent or dependent.

Challenge 2 Hard

Demonstrate if the intersection of two lines in R² is a subspace.

💡 Hint: Consider different conditions under which the lines may or may not intersect.

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