Practice Orthogonal Complement - 27.9 | 27. Inner Product Spaces | Mathematics (Civil Engineering -1)
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27.9 - Orthogonal Complement

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the definition of the orthogonal complement?

💡 Hint: Think about the vectors that satisfy the zero inner product condition.

Question 2

Easy

If W is a subspace of a vector space V, what does W⊥ represent?

💡 Hint: Consider what 'orthogonal' means in terms of the inner product.

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 does the orthogonal complement W⊥ consist of?

  • All vectors in V
  • Vectors orthogonal to W
  • The zero vector only

💡 Hint: Consider how orthogonality relates to inner products.

Question 2

True or False: The orthogonal complement of a subspace W can never include the zero vector.

  • True
  • False

💡 Hint: Think about the property of the zero vector with respect to inner products.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Consider a vector space V = R² and a subspace W = span{(1, 1)}. Find the orthogonal complement W⊥ and describe its geometric representation.

💡 Hint: Use the definition of orthogonality and visualize it graphically.

Question 2

Let W be the set of vectors {(1, 2, 0), (1, 0, 1)} in R³. Determine W⊥ and provide a justification for your findings.

💡 Hint: You may want to set up a system of linear equations based on the orthogonality conditions.

Challenge and get performance evaluation