Practice Rank and Nullity - 24.10 | 24. Vector Space | Mathematics (Civil Engineering -1)
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Rank and Nullity

24.10 - Rank and Nullity

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define Rank.

💡 Hint: Think about linearly independent columns.

Question 2 Easy

What does Nullity represent?

💡 Hint: Relate it to the zeros produced by the matrix.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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

💡 Hint: Think about how columns interact in terms of independence.

Question 2

True or False: The nullity of a matrix represents the number of linearly independent columns.

True
False

💡 Hint: Focus on the definition of nullity.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

For the following matrix A, determine its rank and nullity. Show your process: A = [[1, 0, 0], [0, 1, 0], [0, 0, 0]].

💡 Hint: Identify the leading ones in the rows to determine rank.

Challenge 2 Hard

A matrix B has a rank of 3 and 7 columns. Determine its nullity and explain your reasoning.

💡 Hint: Use the Rank-Nullity theorem relation.

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