Practice Definitions And Concepts (29.1) - Eigenvalues - Mathematics (Civil Engineering -1)
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Definitions and Concepts

Practice - Definitions and Concepts

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Practice Questions

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Question 1 Easy

What is an eigenvalue?

💡 Hint: Think about how a matrix can transform a vector.

Question 2 Easy

Define an eigenvector.

💡 Hint: Look for vectors that keep their direction after transformation.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the characteristic equation used to find eigenvalues?

det(A−λI)=0
det(A)=0
A−λI=0

💡 Hint: Think about how we determine if a matrix is singular.

Question 2

True or False: An eigenvector can be the zero vector.

True
False

💡 Hint: Remember the definition of an eigenvector.

1 more question available

Challenge Problems

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Challenge 1 Hard

Given the matrix C = [[3, 0], [0, 4]], find the eigenvalues and describe their significance for a physical system.

💡 Hint: Use the characteristic polynomial to determine the eigenvalues.

Challenge 2 Hard

Consider a dynamics problem in civil engineering where a building's stiffness matrix K has eigenvalues of 2 and 5. How would these eigenvalues affect the building's response?

💡 Hint: Think about the implications of natural frequencies in structural dynamics.

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