Practice Steps to Find Eigenvectors - 29.2.2 | 29. Eigenvalues | Mathematics (Civil Engineering -1)
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Knowledge

29.2.2 - Steps to Find Eigenvectors

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

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?

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

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.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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.

Challenge and get performance evaluation