4 0 -1 Let A be the following matrix: 0. -1 0 4 (a) Enter its characteristic equation below. Note you must use p as the parameter instead of A, and you must enter your answer as a equation, with the equals sign. -p^3+11*p^2-39*p+45: (b) Enter the eigenvalues of the matrix, including any repetition. For example 16,16,24. 3,3,5 (c) Find the eigenvectors, and then use Gram-Schmidt to find an orthonormal basis for each eigenvalue's eigenspace. Build an orthogonal matrix whose columns are these eigenvectors. Enter this matrix, as a list of row vectors, below. 1 2 3 For example the matrix 4 5 6 would be entered as [1,2,3],[4,5,6],[7,8,9]. 7 8 9
4 0 -1 Let A be the following matrix: 0. -1 0 4 (a) Enter its characteristic equation below. Note you must use p as the parameter instead of A, and you must enter your answer as a equation, with the equals sign. -p^3+11*p^2-39*p+45: (b) Enter the eigenvalues of the matrix, including any repetition. For example 16,16,24. 3,3,5 (c) Find the eigenvectors, and then use Gram-Schmidt to find an orthonormal basis for each eigenvalue's eigenspace. Build an orthogonal matrix whose columns are these eigenvectors. Enter this matrix, as a list of row vectors, below. 1 2 3 For example the matrix 4 5 6 would be entered as [1,2,3],[4,5,6],[7,8,9]. 7 8 9
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![-1
Let A be the following matrix:
3
-1 0
4
(a) Enter its characteristic equation below. Note you must use p as the parameter instead of X,
and you must enter your answer as a equation, with the equals sign.
-p^3+11*p^2-39*p+45:
(b) Enter the eigenvalues of the matrix, including any repetition. For example 16,16,24.
3,3,5
(c) Find the eigenvectors, and then use Gram-Schmidt to find an orthonormal basis for each
eigenvalue's eigenspace.
Build an orthogonal matrix whose columns are these eigenvectors. Enter this matrix, as a list of row
vectors, below.
1 2 3
For example the matrix
4 5 6
would be entered as [1,2,3],[4,5,6],[7,8,9].
7 89
(d) Enter the diagonal matrix P1 AP for your matrix P.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f5c0eab-3a31-4817-8fac-9a126bfc0e32%2F7a44375d-a92d-4459-9b4f-8c9e98a4d2b0%2Fdzqhri_processed.jpeg&w=3840&q=75)
Transcribed Image Text:-1
Let A be the following matrix:
3
-1 0
4
(a) Enter its characteristic equation below. Note you must use p as the parameter instead of X,
and you must enter your answer as a equation, with the equals sign.
-p^3+11*p^2-39*p+45:
(b) Enter the eigenvalues of the matrix, including any repetition. For example 16,16,24.
3,3,5
(c) Find the eigenvectors, and then use Gram-Schmidt to find an orthonormal basis for each
eigenvalue's eigenspace.
Build an orthogonal matrix whose columns are these eigenvectors. Enter this matrix, as a list of row
vectors, below.
1 2 3
For example the matrix
4 5 6
would be entered as [1,2,3],[4,5,6],[7,8,9].
7 89
(d) Enter the diagonal matrix P1 AP for your matrix P.
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