Practice - Row Space, Column Space, and Null Space
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Practice Questions
Test your understanding with targeted questions
Define row space in your own words.
💡 Hint: Think of how you can create new vectors using the rows.
What is the relationship between rank and column space?
💡 Hint: Consider what rank signifies in terms of linear independence.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the row space of a matrix A?
💡 Hint: Consider how you can create vectors from the rows.
True or False: The dimension of the null space increases with the number of linearly independent columns.
💡 Hint: Think about how rank affects null space.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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.
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Reference links
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