Practice Diagonalization Of A Matrix (33.1) - Diagonalization

Practise this section

10 questions

Flashcard drill
4 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
4 questions · about 3 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define a diagonal matrix.
Show hintHide hint
Think about where non-zero elements can be placed in the matrix.
Question 2.
What is an eigenvalue?
Show hintHide hint
Consider what happens to an eigenvector when a linear transformation is applied.
3Question 3.
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
Show hintHide hint
Think about where you can find numbers in a diagonal matrix.
4Question 4.
True or False: A matrix with repeated eigenvalues is always diagonalizable.
- True
- False
Show hintHide hint
Consider what happens when there are fewer eigenvectors than algebraic multiplicities.
Question 5.
Given the matrix A = [3, 2; 4, 5], diagonalize it if possible. Show all steps.
Show hintHide hint
Start with finding the characteristic polynomial.
Question 6.
Determine whether the matrix B = [1, 0; 0, 1] can be diagonalized. Explain why or why not.
Show hintHide hint
What do you notice about the form of this matrix?

6 more questions in this section. Enroll free to practise them all.