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

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9 questions

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6 sample questions

Question 1.
What are the three conditions for a subset to be a subspace?
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Think about the defining properties of a vector space.
Question 2.
Is the set of vectors { (1,0), (0,1), (1,1) } a subspace of ℝ²?
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Verify if zero vector is included and if adding two members gives another member.
3Question 3.
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
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Think of the operations allowed within the vector space.
4Question 4.
True or False: All lines in ℝ² are subspaces.
- True
- False
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Recall the specific properties of subspaces you've learned.
Question 5.
Prove that the span of any set of vectors is a subspace.
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Start by considering what happens when you combine vectors in the span.
Question 6.
Find two vectors in ℝ² that form a line through the origin and demonstrate the closure properties.
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Visualize this on a graph for clarity.

5 more questions in this section. Enroll free to practise them all.