Practice Rank And Nullity (28.5) - Linear Transformations

Practise this section

9 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define 'rank' in the context of linear transformations.
Show hintHide hint
Think about the number of output dimensions.
Question 2.
What does 'nullity' represent?
Show hintHide hint
Consider how many inputs can be mapped to zero.
3Question 3.
What is the rank of a linear transformation?
- Dimension of kernel
- Dimension of image
- Dimension of domain
Show hintHide hint
It relates directly to the output of the transformation.
4Question 4.
True or False: Nullity refers to the dimension of the image.
- True
- False
Show hintHide hint
Remember the definition of each term.
Question 5.
Consider a linear transformation T: R^5 → R^3 where the nullity is 4. What is the rank?
Show hintHide hint
Use the dimension relationship between the spaces.
Question 6.
For a linear transformation represented by a matrix B with 6 columns and an image dimension of 3, what is the kernel dimension?
Show hintHide hint
Recall the Rank-Nullity theorem's formula.

5 more questions in this section. Enroll free to practise them all.