Practice Steps To Find Eigenvectors (29.2.2) - Eigenvalues - Mathematics (Civil Engineering -1)
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Steps to Find Eigenvectors

Practice - Steps to Find Eigenvectors

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the first step to find an eigenvector?

💡 Hint: Think about the equation we formed earlier.

Question 2 Easy

Explain what it means to find the null space.

💡 Hint: What are we trying to solve for in the matrix?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the first step to finding eigenvectors once an eigenvalue has been identified?

Substituting eigenvalue into (A - λI)
Calculating the determinant
Creating a characteristic polynomial

💡 Hint: What do we do after finding eigenvalues to proceed to eigenvectors?

Question 2

True or False: Eigenvectors always correspond to unique eigenvalues.

True
False

💡 Hint: Consider the relationship between values and their corresponding eigenvectors.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the matrix A = [3 0; 0 2], find all eigenvectors for each eigenvalue and explain what they signify about the transformation represented by A.

💡 Hint: Calculate using the substitution method and analyze each step closely.

Challenge 2 Hard

Matrix B has eigenvalues λ = -1 and λ = 4. Derive the eigenvectors and analyze their implications for the transformation behavior regarding compression and stretching.

💡 Hint: Use the eigenvalue-eigenvector relationship carefully to derive implications.

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