25.12 - Singular and Ill-Conditioned Systems
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Practice Questions
Test your understanding with targeted questions
What does it mean when a matrix is singular?
💡 Hint: Consider the properties of determinants.
How is the condition number of a matrix calculated?
💡 Hint: Think about what happens to a matrix and its inverse.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What indicates that a matrix is singular?
💡 Hint: Think about how a determinant reflects the properties of a matrix.
True or False: An ill-conditioned system has a condition number close to 1.
💡 Hint: Reflect on the meaning of sensitivity in systems.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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.
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