Practice Basis Of Eigenvectors (32) - Basis of Eigenvectors - Mathematics (Civil Engineering -1)

Practice: Basis of Eigenvectors

Lesson 32Basis of Eigenvectors

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9 questions

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2 cards from this section. Quick, good the night before a test.
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6 questions · about 4 min · pass mark 70%. Hints available.
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define an eigenvector.
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Think about the relationship between **A**, **v**, and **λ**.
Question 2.
What is the formula for determining the eigenspace associated with an eigenvalue?
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Consider the equation form involving the matrix **A**.
3Question 3.
What defines an eigenvector?
- A vector that can only be zero
- A vector that satisfies Av = λv
- Any random vector
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Focus on the defining equation involving the matrix **A**.
4Question 4.
True or False: The eigenspace of an eigenvalue consists solely of the eigenvector itself.
- True
- False
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Consider whether the eigenspace could have multiple vectors.
Question 5.
Consider the matrix B = [[5, 4], [2, 3]]. Compute its eigenvalues and eigenvectors and discuss their significance in terms of modulating the behavior of a system.
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Set up the characteristic equation and solve for λ.
Question 6.
A matrix has three eigenvalues: 2, 2, and 3. What can you say about its diagonalizability based on geometric and algebraic multiplicities?
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Realize the importance of the corresponding eigenspaces.

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