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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define the term 'rank' in the context of a matrix.
💡 Hint: Think about linear independence.
Question 2
Easy
What does nullity represent?
💡 Hint: Consider vectors that solve Ax = 0.
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 square matrix if all of its columns are linearly independent?
- 0
- 1
- n
💡 Hint: Consider the maximum independence among columns.
Question 2
True or False: Nullity can be negative.
- True
- False
💡 Hint: Dimensions of spaces are always non-negative.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given matrix A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]], determine the rank and nullity.
💡 Hint: Check the relationship between row operations and linear dependence.
Question 2
For a 5x4 matrix with 3 non-zero rows, what can you conclude about its nullity?
💡 Hint: Use the Rank-Nullity theorem to find the answer.
Challenge and get performance evaluation