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21.5.1. Definition
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Mixed questions from across the chapter. Your answers get marked.
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2 cards from this lesson. Good the night before a test.
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- 1.
What is the rank of the matrix [[1, 2], [3, 4]]?
Hint
Count the number of non-zero rows.
- 2.
Define 'rank' in the context of linear algebra.
Hint
Think about independence in vectors.
- 3.
What is the rank of a zero matrix?
- 0
- 1
- 2
Hint
Think about independent vectors in a zero matrix.
- 4.
True or False: The rank of a matrix can be greater than the number of its rows.
- True
- False
Hint
Reflect on the relationship between rank and the dimensions of a matrix.
- 5.
For the matrix [[1, 0, 2], [0, 0, 0], [2, 0, 4], [3, 1, 0]], determine the rank and justify your answer.
Hint
Focus on transforming the matrix to see linear relationships.
- 6.
Given a 5x4 matrix with rank 3, discuss the implications for the system it represents. What does this tell about its solutions?
Hint
Relate rank to unknowns in the system.
Exercises
Total Questions
2
Estimated Time
4 min
Passing Score
70%
Instructions
- Read each question carefully
- You can use hints if you need help
- Complete all questions before submitting
4 more questions available
Enrol freeQuiz
Total Questions
2
Estimated Time
4 min
Passing Score
70%
Instructions
- Read each question carefully
- You can use hints if you need help
- Complete all questions before submitting
1 more question available
Enrol freeChallenge Problems
Total Questions
2
Estimated Time
4 min
Passing Score
70%
Instructions
- Read each question carefully
- You can use hints if you need help
- Complete all questions before submitting