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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define Rank.
💡 Hint: Think about linearly independent columns.
Question 2
Easy
What does Nullity represent?
💡 Hint: Relate it to the zeros produced by the matrix.
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?
- A) The dimension of the null space
- B) The dimension of the column space
- C) The total number of rows
💡 Hint: Think about how columns interact in terms of independence.
Question 2
True or False: The nullity of a matrix represents the number of linearly independent columns.
- True
- False
💡 Hint: Focus on the definition of nullity.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
For the following matrix A, determine its rank and nullity. Show your process: A = [[1, 0, 0], [0, 1, 0], [0, 0, 0]].
💡 Hint: Identify the leading ones in the rows to determine rank.
Question 2
A matrix B has a rank of 3 and 7 columns. Determine its nullity and explain your reasoning.
💡 Hint: Use the Rank-Nullity theorem relation.
Challenge and get performance evaluation