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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the rank of the matrix [[1, 2], [3, 4]]?
💡 Hint: Count the number of non-zero rows.
Question 2
Easy
Define 'rank' in the context of linear algebra.
💡 Hint: Think about independence in vectors.
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 the rank of a zero matrix?
- 0
- 1
- 2
💡 Hint: Think about independent vectors in a zero matrix.
Question 2
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.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation