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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Determine the rank of the following matrix: [1 2; 2 4].
💡 Hint: Look for redundancy between the rows.
Question 2
Easy
List conditions when a set of vectors is considered linearly independent.
💡 Hint: Think about linear combinations and the zero vector.
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
If a matrix has a rank equal to its number of columns, what can we say about its column vectors?
- They are linearly dependent
- They are linearly independent
- They are not related
💡 Hint: Recall the definition of rank.
Question 2
True or False: A set containing the zero vector can still be linearly independent.
- True
- False
💡 Hint: Consider the implications of the zero vector in linear combinations.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider a matrix A with vectors [(1, 2), (2, 4), (3, 6), (4, 8)]. What is its rank and what does this imply about the vectors?
💡 Hint: Check if any vector can be produced as a linear combination of the others.
Question 2
If a system of equations is determined by vectors in R^6, can any matrix formed from them have a rank greater than 6? Justify your answer.
💡 Hint: Review the relationship between the rank of a matrix and its dimensional properties.
Challenge and get performance evaluation