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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define row space in your own words.
💡 Hint: Think of how you can create new vectors using the rows.
Question 2
Easy
What is the relationship between rank and column space?
💡 Hint: Consider what rank signifies in terms of linear independence.
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 row space of a matrix A?
💡 Hint: Consider how you can create vectors from the rows.
Question 2
True or False: The dimension of the null space increases with the number of linearly independent columns.
- True
- False
💡 Hint: Think about how rank affects null space.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a matrix A = [[2, 4, -2], [1, 3, -1]], find its row space, column space, and null space.
💡 Hint: Start by determining the rank and then use it to find the nullity.
Question 2
Prove that adding a scalar multiple of one row to another does not change the row space.
💡 Hint: Think about how linear combinations work in a vector space.
Challenge and get performance evaluation