Practice Ill-conditioned System (25.12.2) - Solutions of Linear Systems: Existence, Uniqueness, General Form
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Ill-Conditioned System

Practice - Ill-Conditioned System

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Practice Questions

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Question 1 Easy

Define an ill-conditioned system.

💡 Hint: Consider sensitivity to changes in data.

Question 2 Easy

What does a condition number of 1 indicate?

💡 Hint: Think about stability and sensitivity.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What happens in an ill-conditioned system?

Small changes have minor effects
Small changes lead to large errors
The system is always solvable

💡 Hint: Consider how sensitivity impacts results.

Question 2

An ill-conditioned system typically has a condition number that is ____.

Close to 1
Greater than 1
Less than 1

💡 Hint: Think about what condition numbers signify.

1 more question available

Challenge Problems

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Challenge 1 Hard

A civil engineering project faces a potential ill-conditioned system with a high condition number. Discuss the implications for construction safety and suggest three corrective strategies to address potential issues.

💡 Hint: Think about the roles of calculations and safety in construction.

Challenge 2 Hard

A system has a condition number of 1000. What does this imply? Provide an analysis of how this impacts solutions and engineering decisions.

💡 Hint: Reflect on what sensitivity implies for real-world applications.

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