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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does it mean when a matrix is singular?
💡 Hint: Consider the properties of determinants.
Question 2
Easy
How is the condition number of a matrix calculated?
💡 Hint: Think about what happens to a matrix and its inverse.
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 indicates that a matrix is singular?
- det(A) = 1
- det(A) = 0
- det(A) < 0
💡 Hint: Think about how a determinant reflects the properties of a matrix.
Question 2
True or False: An ill-conditioned system has a condition number close to 1.
- True
- False
💡 Hint: Reflect on the meaning of sensitivity in systems.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the matrix A = [[1, 2], [2, 4]], determine if A is singular. Why or why not?
💡 Hint: Consider the relationship between the rows or columns.
Question 2
If κ(A) = 50, explain what this implies about the stability of a linear system using A.
💡 Hint: Reflect on external factors that could affect the model.
Challenge and get performance evaluation