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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the rank of a matrix with all zero rows?
💡 Hint: Think about the definition of linearly independent vectors.
Question 2
Easy
If a matrix has 3 rows and 2 linearly independent rows, what is its rank?
💡 Hint: Remember, rank corresponds to independent rows.
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 matrix?
- Number of rows
- Number of columns
- Maximum number of linearly independent vectors
💡 Hint: Focus on the meaning of independence in vectors.
Question 2
True or False: A matrix with more rows than columns can always have rank equal to the number of rows.
- True
- False
💡 Hint: Consider the relationship of linear dependence.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the matrix A = [[2, 4, 1], [6, 10, 3], [4, 8, 2]], find its rank by row-reduction and explain your steps.
💡 Hint: Focus on identifying dependent rows.
Question 2
Demonstrate the impact of rank on the solutions of the linear system represented by A. If rank(A) < rank([A | b]), what can you conclude?
💡 Hint: Think about the augmentation of the matrix and about linear equations.
Challenge and get performance evaluation