Practice Eigenvalues and Eigenvectors Review - 33.2 | 33. Diagonalization | Mathematics (Civil Engineering -1)
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Eigenvalues and Eigenvectors Review

33.2 - Eigenvalues and Eigenvectors Review

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the definition of an eigenvalue?

💡 Hint: Think of the transformation of vectors.

Question 2 Easy

How do you find eigenvalues for a matrix?

💡 Hint: Calculate the determinant and set it to zero.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does an eigenvalue represent?

A vector that changes direction
A scalar that indicates scaling of an eigenvector
A constant value of the matrix

💡 Hint: Think about what happens when a vector is transformed.

Question 2

The equation Av = λv is used to define which concept?

True
False

💡 Hint: Recall the definition of eigenvalues and eigenvectors.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the matrix B = [[5, 4], [0, 2]], find its eigenvalues and eigenvectors, and discuss its diagonalizability.

💡 Hint: Start with the characteristic equation.

Challenge 2 Hard

Consider the matrix C = [[1, 1], [0, 1]]. Investigate if it's diagonalizable and explain why or why not.

💡 Hint: Check the multiplicities!

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