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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a diagonal matrix in your own words.
💡 Hint: Consider where the non-zero elements can be located.
Question 2
Easy
If a diagonal matrix has three non-zero elements, what is its rank?
💡 Hint: Remember, rank is about counting non-zero diagonal elements.
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 the diagonal matrix D = [[3, 0, 0], [0, 4, 0], [0, 0, 0]]?
- 3
- 2
- 1
💡 Hint: Count the non-zero elements on the diagonal.
Question 2
True or False: A zero matrix is considered a diagonal matrix.
- True
- False
💡 Hint: Reflect on the definition of diagonal matrices.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the diagonal matrix D = [[7, 0, 0], [0, 5, 0], [0, 0, -3]], calculate the rank and explain your method.
💡 Hint: Refer to how many diagonal entries you see that are non-zero.
Question 2
If you manipulate a diagonal matrix by setting one of its non-zero diagonal entries to zero, how would that change its rank? Provide an example.
💡 Hint: Think about how rank is determined by counting non-zeros.
Challenge and get performance evaluation