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29. Eigenvalues
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11 questions on this section. Wrong answers show you what to read again.
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Mixed questions from across the chapter. Your answers get marked.
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3 cards from this lesson. Good the night before a test.
Try these first
- 1.
Define an eigenvalue in your own words.
Hint
Think about how it affects a vector's length.
- 2.
What does the characteristic polynomial help us find?
Hint
Consider what needs to be set to zero.
- 3.
What mathematical equation is used to find eigenvalues of a matrix?
Hint
Recall how eigenvalues are defined.
- 4.
Eigenvectors can only exist for real eigenvalues.
- True
- False
Hint
What about applications in electrical or dynamic systems?
- 5.
Given a matrix A = [[4, 1, 1], [1, 3, 1], [1, 1, 2]], find its eigenvalues and eigenvectors.
Hint
Construct the determinant and remember to find the null space for vectors.
- 6.
How do eigenvalues influence the design of a bridge subject to dynamic loads? Discuss.
Hint
Connect your answers with structural integrity and loading responses.
Exercises
Total Questions
2
Estimated Time
4 min
Passing Score
70%
Instructions
- Read each question carefully
- You can use hints if you need help
- Complete all questions before submitting
4 more questions available
Enrol freeQuiz
Total Questions
2
Estimated Time
4 min
Passing Score
70%
Instructions
- Read each question carefully
- You can use hints if you need help
- Complete all questions before submitting
1 more question available
Enrol freeChallenge Problems
Total Questions
2
Estimated Time
4 min
Passing Score
70%
Instructions
- Read each question carefully
- You can use hints if you need help
- Complete all questions before submitting