Practice Rank And Nullity (24.10) - Vector Space - Mathematics (Civil Engineering -1)

Practise this section

9 questions

Flashcard drill
3 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.
Show hintHide hint
Think about linearly independent columns.
Question 2.
What does Nullity represent?
Show hintHide hint
Relate it to the zeros produced by the matrix.
3Question 3.
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
Show hintHide hint
Think about how columns interact in terms of independence.
4Question 4.
True or False: The nullity of a matrix represents the number of linearly independent columns.
- True
- False
Show hintHide hint
Focus on the definition of nullity.
Question 5.
For the following matrix A, determine its rank and nullity. Show your process: A = [[1, 0, 0], [0, 1, 0], [0, 0, 0]].
Show hintHide hint
Identify the leading ones in the rows to determine rank.
Question 6.
A matrix B has a rank of 3 and 7 columns. Determine its nullity and explain your reasoning.
Show hintHide hint
Use the Rank-Nullity theorem relation.

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