Consider the following matrix A= -3 4 4 3 (a) (8 points) Diagonalize A. (b) (4...
Consider the following matrix
A= -3 4
4 3
(a) (8 points) Diagonalize A.
(b) (4 points) Using your result of part (a) compute A^20 . You must perform the multiplication to receive a single matrix as a result but you don’t have to simplify the high powers in the entries. Your result should look like A^20 = 5^b × B for some matrix B and power b.
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Consider the following matrix
A= -3 4
4 3
(a) (8 points) Diagonalize A.
(b) (4...
Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. 2...
Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. 2 2 -4 - 1 5 -4 ; 2 = 3,8 -2 7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. 3 0 0 For P = D= 0 3 0 0 0 8 (Simplify your answer.) B. 3 00 For P = D = 0 8 0 0 0 8 (Simplify your answer.)...
4. Find all the eigenvalues and eigenvectors of the following 3 by 3 matrix. If it...
4. Find all the eigenvalues and eigenvectors of the following 3 by 3 matrix. If it is possible to diagonalized, then diagonalize the matrix. If it is not possible to diagonalize, then explain why? Show all the work. (20 points) 54 -5 A = 1 0 LO 1 1 - 1 -1
16.-1 points poolelinalg4 5.4.006.nva My Notes Ask Your Teache Orthogonally diagonalize the matrix below by finding an orthogonal matrix Q and a diagonal matrix D such that QT AQ = D separated list.)...
16.-1 points poolelinalg4 5.4.006.nva My Notes Ask Your Teache Orthogonally diagonalize the matrix below by finding an orthogonal matrix Q and a diagonal matrix D such that QT AQ = D separated list.) Enter each matrix in the form row 1 row 2 where each row is a comma- 3 3 0 0 4 3 Need Help? 17. 1 points poolelinalg4 5.4.009 nva My Notes Ask Your Teacher Orthogonally diagonalize the matrix below by finding an orthogonal matrix Q and...
Consider the following matrices 2. .6 6 .9 A2 Ag (a) Diagonalize each matrix by writing...
Consider the following matrices 2. .6 6 .9 A2 Ag (a) Diagonalize each matrix by writing A SAS-1 (b) For each of these three matrices, compute the limit Ak-SNS-1 as k-+ 00 if it exists. (c) Suppose A is an n x n matrix that is diagonalizable (so it has n linearly independent eigenvectors). What must be true for the limit Ak to exist as k → oo? What is needed for Ak-+ O? Justify your answer.
Thank you! Diagonalize the following matrix. The real eigenvalues are given to the right of the...
Thank you!
Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. 1 18 12 -1 10 4 : 1 = 3,4 1 -6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 300 For P=D=030 0 0 4 0 B. 3 0 0 For P= D= 040 004 OC. The matrix cannot be diagonalized.
6. (5 points) Suppose the elementary matrix E is of this form (a) Compute the matrix...
6. (5 points) Suppose the elementary matrix E is of this form (a) Compute the matrix multiplication EB (b) Compute the determinant of EB using the cofactor expansion along the 1st row of the matrix, and show that the determinant is equal to -det(B) (MUST use the cofactor expansion, no points will be given for other meth- ods.) Hint: Same, don't expand everything out, you will be drown in a sea of bij, you should look at the cofactor expansion...
(1 point) Consider the matrix -5 7 8-9 20 -30 8-3 -15 -19 9 -4 10-11 5-8 (a) On the matrix above,...
(1 point) Consider the matrix -5 7 8-9 20 -30 8-3 -15 -19 9 -4 10-11 5-8 (a) On the matrix above, perform the row operation R1 15 R1 . The new matrix is: (b) Using the matrix obtained in your answer for part (a) as the initial matrix, next perform the row operations () R3 R3 15R1, (iii) R4→R4+10R1. The new matrix is: (c) Using the matrix obtained in your answer for part (b) as the initial matrix, next...
Q3 (8 points) In the following A is a 3 × 4 matrix (3 rows, 4...
Q3 (8 points) In the following A is a 3 × 4 matrix (3 rows, 4 columns) and the coefficient matrix of a system of linear equations. A. Find an example of such a matrix A and a vector b such that the system with augmented matrix [A | b] has no solution. Justify your answer. B. Find an example of such a matrix A and a vector b such that the system with augmented matrix [A | b] has...
4. Consider the following matrix [1 0 -27 A=000 L-2 0 4] (a) (3 points) Find...
4. Consider the following matrix [1 0 -27 A=000 L-2 0 4] (a) (3 points) Find the characteristic polynomial of A. (b) (4 points) Find the eigenvalues of A. Give the algebraic multiplicity of each eigenvalue (c) (8 points) Find the eigenvectors corresponding to the eigenvalues found in part (b). (d) (4 points) Give a diagonal matrix D and an invertible matrix P such that A = PDP-1 (e) (6 points) Compute P-and verify that A= PDP- (show your steps).
2. Let A be the matrix shown below A= a.) (8 points) Find the matrix P...
2. Let A be the matrix shown below A= a.) (8 points) Find the matrix P that diagonalizes A. b.) (2 points) Using your result from part a, find A. You must show how part a was used for credit.
Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. 2 2 -4 - 1 5 -4 ; 2 = 3,8 -2 7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. 3 0 0 For P = D= 0 3 0 0 0 8 (Simplify your answer.) B. 3 00 For P = D = 0 8 0 0 0 8 (Simplify your answer.)...
4. Find all the eigenvalues and eigenvectors of the following 3 by 3 matrix. If it is possible to diagonalized, then diagonalize the matrix. If it is not possible to diagonalize, then explain why? Show all the work. (20 points) 54 -5 A = 1 0 LO 1 1 - 1 -1
16.-1 points poolelinalg4 5.4.006.nva My Notes Ask Your Teache Orthogonally diagonalize the matrix below by finding an orthogonal matrix Q and a diagonal matrix D such that QT AQ = D separated list.) Enter each matrix in the form row 1 row 2 where each row is a comma- 3 3 0 0 4 3 Need Help? 17. 1 points poolelinalg4 5.4.009 nva My Notes Ask Your Teacher Orthogonally diagonalize the matrix below by finding an orthogonal matrix Q and...
Consider the following matrices 2. .6 6 .9 A2 Ag (a) Diagonalize each matrix by writing A SAS-1 (b) For each of these three matrices, compute the limit Ak-SNS-1 as k-+ 00 if it exists. (c) Suppose A is an n x n matrix that is diagonalizable (so it has n linearly independent eigenvectors). What must be true for the limit Ak to exist as k → oo? What is needed for Ak-+ O? Justify your answer.
Thank you!
Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. 1 18 12 -1 10 4 : 1 = 3,4 1 -6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 300 For P=D=030 0 0 4 0 B. 3 0 0 For P= D= 040 004 OC. The matrix cannot be diagonalized.
6. (5 points) Suppose the elementary matrix E is of this form (a) Compute the matrix multiplication EB (b) Compute the determinant of EB using the cofactor expansion along the 1st row of the matrix, and show that the determinant is equal to -det(B) (MUST use the cofactor expansion, no points will be given for other meth- ods.) Hint: Same, don't expand everything out, you will be drown in a sea of bij, you should look at the cofactor expansion...
(1 point) Consider the matrix -5 7 8-9 20 -30 8-3 -15 -19 9 -4 10-11 5-8 (a) On the matrix above, perform the row operation R1 15 R1 . The new matrix is: (b) Using the matrix obtained in your answer for part (a) as the initial matrix, next perform the row operations () R3 R3 15R1, (iii) R4→R4+10R1. The new matrix is: (c) Using the matrix obtained in your answer for part (b) as the initial matrix, next...
Q3 (8 points) In the following A is a 3 × 4 matrix (3 rows, 4 columns) and the coefficient matrix of a system of linear equations. A. Find an example of such a matrix A and a vector b such that the system with augmented matrix [A | b] has no solution. Justify your answer. B. Find an example of such a matrix A and a vector b such that the system with augmented matrix [A | b] has...
4. Consider the following matrix [1 0 -27 A=000 L-2 0 4] (a) (3 points) Find the characteristic polynomial of A. (b) (4 points) Find the eigenvalues of A. Give the algebraic multiplicity of each eigenvalue (c) (8 points) Find the eigenvectors corresponding to the eigenvalues found in part (b). (d) (4 points) Give a diagonal matrix D and an invertible matrix P such that A = PDP-1 (e) (6 points) Compute P-and verify that A= PDP- (show your steps).
2. Let A be the matrix shown below A= a.) (8 points) Find the matrix P that diagonalizes A. b.) (2 points) Using your result from part a, find A. You must show how part a was used for credit.
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