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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define the rank of a matrix.
💡 Hint: Think about linear independence.
Question 2
Easy
What is echelon form?
💡 Hint: Visualize a staircase.
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 definition of rank?
- A number of non-zero elements in a matrix
- Maximum number of linearly independent rows or columns
- The total number of rows and columns in a matrix
💡 Hint: Focus on linear independence.
Question 2
True or False: Rank can only be determined using echelon form.
- True
- False
💡 Hint: Think about different methods available to find rank.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the \(4 \times 4\) matrix \(C = \begin{bmatrix} 1 & 0 & 0 & 5 \ 0 & 0 & 0 & 0 \ 0 & 2 & 1 & 3 \ 0 & 0 & 0 & 0 \end{bmatrix}\), find the rank after performing row reduction.
💡 Hint: Focus on reducing the matrix to echelon form first.
Question 2
A \(2 \times 3\) matrix \(D\) has a rank of 2. If you added a third row that is a linear combination of the existing rows, what would the new rank be?
💡 Hint: Consider the implications of linear combinations on independence.
Challenge and get performance evaluation