Practice Quotient Vector Spaces - 24.14 | 24. Vector Space | Mathematics (Civil Engineering -1)
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24.14 - Quotient Vector Spaces

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define a quotient vector space.

💡 Hint: Remember the structure and notation of V/W.

Question 2

Easy

What is an equivalence class?

💡 Hint: Think about vectors differing by elements in W.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is a quotient vector space?

  • A vector space created from two vectors
  • The set of equivalence classes of a vector space formed by a subspace
  • A scalar operation in a vector space

💡 Hint: Think about the relationship between vector spaces and their subsets.

Question 2

True or False: The operations in quotient spaces do not maintain the properties of a vector space.

  • True
  • False

💡 Hint: Recall how we define addition and scalar multiplication in quotient spaces.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Let V = R^3 and W = {(x, y, 0) | x, y ∈ R}. Prove that the dimension of the quotient space R^3/W is 1.

💡 Hint: Use the dimension theorem for vector spaces and consider the direct relationship between dimensions.

Question 2

Consider the subspace W of P(x), the polynomial space of degree ≤ n. Determine how the quotient space P(x)/W changes with varying dimensions of W.

💡 Hint: Analyze how dimensions correlate and affect the resulting polynomial set.

Challenge and get performance evaluation