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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define 'rank' in the context of linear transformations.
💡 Hint: Think about the number of output dimensions.
Question 2
Easy
What does 'nullity' represent?
💡 Hint: Consider how many inputs can be mapped to zero.
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 linear transformation?
- Dimension of kernel
- Dimension of image
- Dimension of domain
💡 Hint: It relates directly to the output of the transformation.
Question 2
True or False: Nullity refers to the dimension of the image.
- True
- False
💡 Hint: Remember the definition of each term.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider a linear transformation T: R^5 → R^3 where the nullity is 4. What is the rank?
💡 Hint: Use the dimension relationship between the spaces.
Question 2
For a linear transformation represented by a matrix B with 6 columns and an image dimension of 3, what is the kernel dimension?
💡 Hint: Recall the Rank-Nullity theorem's formula.
Challenge and get performance evaluation