Home › Quizzes › Linear Independence

Linear Independence

This quiz is designed to assess your understanding of the concept of linear independence in linear algebra.

14 Questions Published
Play Quiz Practise this topic out loud

Questions

Question 1 Multiple Choice (Single Answer)

Which of the following sets of vectors is linearly independent in the vector space of polynomials of degree 2 or less?

  1. {(1, 0, 0), (0, 1, 0), (0, 0, 1)}
  2. {(1, 1, 0), (1, 0, 1), (0, 1, 1)}
  3. {(1, 2, 3), (4, 5, 6), (7, 8, 9)}
  4. {(1, 0, 1), (0, 1, 1), (1, 1, 1)}
Question 2 Multiple Choice (Single Answer)

Determine whether the following set of vectors is linearly independent in the vector space of real numbers:

  1. {(1, 2, 3), (4, 5, 6), (7, 8, 9)}
  2. {(1, 0, 1), (0, 1, 1), (1, 1, 1)}
  3. {(1, 2, 3), (2, 4, 6), (3, 6, 9)}
  4. {(1, 1, 0), (1, 0, 1), (0, 1, 1)}
Question 3 Multiple Choice (Single Answer)

Consider the following set of vectors in the vector space of continuous functions on the interval [0, 1]:

  1. {(1, 0, 0), (0, 1, 0), (0, 0, 1)}
  2. {(1, 1, 0), (1, 0, 1), (0, 1, 1)}
  3. {(1, 2, 3), (4, 5, 6), (7, 8, 9)}
  4. {(1, 0, 1), (0, 1, 1), (1, 1, 1)}
Question 4 Multiple Choice (Single Answer)

Determine whether the following set of vectors is linearly independent in the vector space of complex numbers:

  1. {(1, 2i), (3, 4i), (5, 6i)}
  2. {(1, i), (2, 2i), (3, 3i)}
  3. {(1, 2), (3, 4), (5, 6)}
  4. {(1, 1), (1, 0), (0, 1)}
Question 5 Multiple Choice (Single Answer)

Consider the following set of vectors in the vector space of polynomials of degree 3 or less:

  1. {(1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1)}
  2. {(1, 1, 1, 1), (1, 0, 1, 0), (1, 0, 0, 1), (0, 1, 0, 1)}
  3. {(1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12)}
  4. {(1, 0, 1, 1), (0, 1, 1, 1), (1, 1, 1, 1)}
Question 6 Multiple Choice (Single Answer)

Determine whether the following set of vectors is linearly independent in the vector space of real numbers:

  1. {(1, 2, 3), (4, 5, 6), (7, 8, 9)}
  2. {(1, 0, 1), (0, 1, 1), (1, 1, 1)}
  3. {(1, 2, 3), (2, 4, 6), (3, 6, 9)}
  4. {(1, 1, 0), (1, 0, 1), (0, 1, 1)}
Question 7 Multiple Choice (Single Answer)

Consider the following set of vectors in the vector space of continuous functions on the interval [0, 1]:

  1. {(1, 0, 0), (0, 1, 0), (0, 0, 1)}
  2. {(1, 1, 0), (1, 0, 1), (0, 1, 1)}
  3. {(1, 2, 3), (4, 5, 6), (7, 8, 9)}
  4. {(1, 0, 1), (0, 1, 1), (1, 1, 1)}
Question 8 Multiple Choice (Single Answer)

Determine whether the following set of vectors is linearly independent in the vector space of complex numbers:

  1. {(1, 2i), (3, 4i), (5, 6i)}
  2. {(1, i), (2, 2i), (3, 3i)}
  3. {(1, 2), (3, 4), (5, 6)}
  4. {(1, 1), (1, 0), (0, 1)}
Question 9 Multiple Choice (Single Answer)

Consider the following set of vectors in the vector space of polynomials of degree 3 or less:

  1. {(1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1)}
  2. {(1, 1, 1, 1), (1, 0, 1, 0), (1, 0, 0, 1), (0, 1, 0, 1)}
  3. {(1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12)}
  4. {(1, 0, 1, 1), (0, 1, 1, 1), (1, 1, 1, 1)}
Question 10 Multiple Choice (Single Answer)

Determine whether the following set of vectors is linearly independent in the vector space of real numbers:

  1. {(1, 2, 3), (4, 5, 6), (7, 8, 9)}
  2. {(1, 0, 1), (0, 1, 1), (1, 1, 1)}
  3. {(1, 2, 3), (2, 4, 6), (3, 6, 9)}
  4. {(1, 1, 0), (1, 0, 1), (0, 1, 1)}
Question 11 Multiple Choice (Single Answer)

Consider the following set of vectors in the vector space of continuous functions on the interval [0, 1]:

  1. {(1, 0, 0), (0, 1, 0), (0, 0, 1)}
  2. {(1, 1, 0), (1, 0, 1), (0, 1, 1)}
  3. {(1, 2, 3), (4, 5, 6), (7, 8, 9)}
  4. {(1, 0, 1), (0, 1, 1), (1, 1, 1)}
Question 12 Multiple Choice (Single Answer)

Determine whether the following set of vectors is linearly independent in the vector space of complex numbers:

  1. {(1, 2i), (3, 4i), (5, 6i)}
  2. {(1, i), (2, 2i), (3, 3i)}
  3. {(1, 2), (3, 4), (5, 6)}
  4. {(1, 1), (1, 0), (0, 1)}
Question 13 Multiple Choice (Single Answer)

Consider the following set of vectors in the vector space of polynomials of degree 3 or less:

  1. {(1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1)}
  2. {(1, 1, 1, 1), (1, 0, 1, 0), (1, 0, 0, 1), (0, 1, 0, 1)}
  3. {(1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12)}
  4. {(1, 0, 1, 1), (0, 1, 1, 1), (1, 1, 1, 1)}
Question 14 Multiple Choice (Single Answer)

Determine whether the following set of vectors is linearly independent in the vector space of real numbers:

  1. {(1, 2, 3), (4, 5, 6), (7, 8, 9)}
  2. {(1, 0, 1), (0, 1, 1), (1, 1, 1)}
  3. {(1, 2, 3), (2, 4, 6), (3, 6, 9)}
  4. {(1, 1, 0), (1, 0, 1), (0, 1, 1)}
← Back to Quizzes