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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

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

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.4: Orthogonal Diagonalization Of Symmetric Matrices
Problem 27EQ
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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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