Practice Subspace (21.8.2) - Linear Algebra - Mathematics (Civil Engineering -1)

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6 sample questions

Question 1.
Define a subspace in your own words.
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Think about closure under operations.
Question 2.
What is meant by the basis of a subspace?
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Consider how you can represent all vectors in the subspace.
3Question 3.
What is a subspace?
- A larger space than a vector space
- A subset of a vector space that is itself a vector space
- A collection of all the linear transformations
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Think about properties shared with the original space.
4Question 4.
True or False: Every subset of a vector space is a subspace.
- True
- False
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Consider the criteria for being a subspace.
Question 5.
Given the vectors (1, 2, 3) and (2, 4, 6), determine if they form a basis for R³ and justify why or why not.
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Consider the independence of these vectors.
Question 6.
Prove that the set of all vectors in R² that can be expressed as (x, 0) for any real number x forms a subspace.
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Check that adding any two such vectors still results in a vector of the same form.

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