multiplicity of each eigenvalue of A. Find a basis for the eigenspace of the eigenvalue 1 =7 . Do this partially by using the appropriate technology, by clearly showing the following steps: 1) Clearly write the matrix equation you set up to find the eigenvector 2) Use Octave to rref the matrix. Include Octave output. Performing ro is not appropriate and will result in a zero for this problem. 3) Interpret the output, writing a parameterized solution 4) Use that solution to write the form of the eigenspace 5) Give a basis for the space O State the geometric multiplicity of 2 = 7. %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
7 0 0 0
-3 2 0 0
A =
0 1 7 0
Let
|-6 1 0 7
(a) The eigenvalues of this matrix are easily obtainable by inspection. Quickly state the algebraic
multiplicity of each eigenvalue of A.
(b) Find a basis for the eigenspace of the eigenvalue 1 =7. Do this partially by hand, partially
using the appropriate technology, by clearly showing the following steps:
1) Clearly write the matrix equation you set up to find the eigenvector(s)
2) Use Octave to rref the matrix. Include Octave output. Performing row reduction by hand
is not appropriate and will result in a zero for this problem.
3) Interpret the output, writing a parameterized solution
4) Use that solution to write the form of the eigenspace
5) Give a basis for the space
(c) State the geometric multiplicity of 1 = 7
Transcribed Image Text:7 0 0 0 -3 2 0 0 A = 0 1 7 0 Let |-6 1 0 7 (a) The eigenvalues of this matrix are easily obtainable by inspection. Quickly state the algebraic multiplicity of each eigenvalue of A. (b) Find a basis for the eigenspace of the eigenvalue 1 =7. Do this partially by hand, partially using the appropriate technology, by clearly showing the following steps: 1) Clearly write the matrix equation you set up to find the eigenvector(s) 2) Use Octave to rref the matrix. Include Octave output. Performing row reduction by hand is not appropriate and will result in a zero for this problem. 3) Interpret the output, writing a parameterized solution 4) Use that solution to write the form of the eigenspace 5) Give a basis for the space (c) State the geometric multiplicity of 1 = 7
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