Practice Diagonalization of a Matrix - 33.1 | 33. Diagonalization | Mathematics (Civil Engineering -1)
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Diagonalization of a Matrix

33.1 - Diagonalization of a Matrix

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define a diagonal matrix.

💡 Hint: Think about where non-zero elements can be placed in the matrix.

Question 2 Easy

What is an eigenvalue?

💡 Hint: Consider what happens to an eigenvector when a linear transformation is applied.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is a diagonal matrix?

A matrix with all elements zero
Non-zero elements only along the diagonal
All non-diagonal elements are non-zero

💡 Hint: Think about where you can find numbers in a diagonal matrix.

Question 2

True or False: A matrix with repeated eigenvalues is always diagonalizable.

True
False

💡 Hint: Consider what happens when there are fewer eigenvectors than algebraic multiplicities.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the matrix A = [3, 2; 4, 5], diagonalize it if possible. Show all steps.

💡 Hint: Start with finding the characteristic polynomial.

Challenge 2 Hard

Determine whether the matrix B = [1, 0; 0, 1] can be diagonalized. Explain why or why not.

💡 Hint: What do you notice about the form of this matrix?

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