# Eigenvalue and Eigenvector in Linear Algebra Lesson Plans Chapter Exam

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Question 1
1.
Which of the following statements is **NOT** true?

#### Question 2 2. Find the eigenvectors associated with the eigenvalue of 4 for the following matrix.

#### Question 3 3. In order to find a matrix's eigenvectors, we solve the following equation. Which of this equation's variables represents the eigenvectors?

#### Question 4 4. Find the eigenvectors associated with the eigenvalue of 0 for the following matrix.

#### Question 5 5. Find the eigenvectors associated with the eigenvalue of 4 for the following matrix.

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#### Question 6 6. The matrix, A, is a _____.

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Question 7
7.
If the eigenvector of a matrix is the vector, *v*1, shown below, then the length of *v*1 is _____.

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Question 8
8.
To diagonalize a matrix, A, we calculate Pt AP. For the normalized eigenvectors, *u*1 and *u*2, the matrix, P, is given by _____.

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Question 9
9.
For the eigenvector, *v*, the normalized eigenvector, *u*, is _____.

#### Question 10 10. To diagonalize a symmetric matrix, A, we calculate Pt AP. The result is the matrix, D, where D is the diagonal matrix shown. The eigenvalues of A are _____.

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Question 11
11.
Find all the eigenvalues of the following 2x2 matrix (**A**).

#### Question 12 12. Let's say you work a problem where you find all the eigenvalues of a 5x5 matrix. How many eigenvalues will you find?

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Question 13
13.
Find all the eigenvalues for the following 2x2 matrix (**A**).

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Question 14
14.
Find all the eigenvalues for the following 3x3 matrix (**A**).

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Question 15
15.
What is the general equation we use to find the eigenvalues of any *nxn* matrix (A)?

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#### Question 16 16. What determined the degree of the characteristic polynomial?

#### Question 17 17. Which of the following matrices are in diagonal form?

#### Question 18 18. In order for a matrix to have a diagonal form, we must be able to consider values for which the characterstic polynomial is equal to

#### Question 19 19. What sort of matrices may be diagonalized.

#### Question 20 20. The values in a diagonal form of a matrix are the _____ of the matrix.

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#### Question 21 21. One of the eigenvalues of the following matrix is -2. Find the corresponding eigenvector where we put 1 in for the first parameter of the vector.

#### Question 22 22. How many eigenvectors does a 2 by 2 matrix have?

#### Question 23 23. Find the eigenvalues of the following matrix.

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Question 24
24.
For any real number *x*, the following is an eigenvector of a matrix *A*. Find its unit eigenvector.

#### Question 25 25. How many eigenvalues does a 2 by 2 matrix have?

#### Eigenvalue and Eigenvector in Linear Algebra Lesson Plans Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!