Practice Coordinates of a Vector - 24.8 | 24. Vector Space | Mathematics (Civil Engineering -1)
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24.8 - Coordinates of a Vector

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

If vector v = (5, 2) is expressed in terms of basis B = {(1, 0), (0, 1)}, what is the coordinate vector?

💡 Hint: Identify the coefficients based on the basis representation.

Question 2

Easy

Express vector v = (3, 3) in terms of basis B = {(1, 1), (1, 0)}. What is the coordinate vector?

💡 Hint: Think about how many times you need each basis vector.

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Interactive Quizzes

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

Question 1

What is a coordinate vector?

  • A representation of a vector in a visual form
  • The tuple of coefficients expressing a vector in terms of a basis
  • A way to graph vectors

💡 Hint: Think about representing vectors in terms of their basis.

Question 2

True or False: All vectors in a vector space can be expressed in terms of the same basis.

  • True
  • False

💡 Hint: Recall the properties of vector spaces and their bases.

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Challenge Problems

Push your limits with challenges.

Question 1

Given basis B = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} and vector v = (5, 7, 2), compute and explain the coordinates of vector v.

💡 Hint: Use the definition of coordinate vectors and linear combinations.

Question 2

If we alter the basis to B' = {(2, 0), (0, 3)} and have vector v = (6, 9), find the coordinates of v in this new basis.

💡 Hint: Express the vector in terms of the new basis and solve for the coefficients.

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