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We have the following matrix where each column is identical: a a a A =| b b 1. Since this matrix is not full rank, it is singular and thus å = 0 is an eigenvalue. Find two linearly independent eigenvectors of A other libraries to check your work, but please show the steps of your would-be corresponding to 1 = 0. You may use SymPy computations. 2. 1 = 0 is also an eigenvalue of A'. Find two linearly independent eigenvectors of A' corresponding to 1 = 0.

We have the following matrix where each column is identical: a a a A =| b b 1. Since this matrix is not full rank, it is singular and thus å = 0 is an eigenvalue. Find two linearly independent eigenvectors of A other libraries to check your work, but please show the steps of your would-be corresponding to 1 = 0. You may use SymPy computations. 2. 1 = 0 is also an eigenvalue of A'. Find two linearly independent eigenvectors of A' corresponding to 1 = 0.

Advanced Engineering Mathematics
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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We have the following matrix where each column is identical: a а а А — b 1. Since this matrix is not full rank, it is singular and thus 1 = 0 is an eigenvalue. Find two linearly independent eigenvectors of A corresponding to 1 = 0. You may use SymPy or other libraries to check your work, but please show the steps of your would-be computations. 2. 1 = 0 is also an eigenvalue of A". Find two linearly independent eigenvectors of AT corresponding to 1 = 0. 3. A and A' have three eigenvalues each, but 1 = 0 makes up two of the three since it corresponds to two linearly independent eigenvectors for both matrices. Find the third eigenvalue of A and A' by looking at the trace of A. 4. Show that (a, b, c) is the corresponding eigenvector of A and that (1, 1, 1) is the corresponding eigenvector of A' .
Transcribed Image Text:We have the following matrix where each column is identical: a а а А — b 1. Since this matrix is not full rank, it is singular and thus 1 = 0 is an eigenvalue. Find two linearly independent eigenvectors of A corresponding to 1 = 0. You may use SymPy or other libraries to check your work, but please show the steps of your would-be computations. 2. 1 = 0 is also an eigenvalue of A". Find two linearly independent eigenvectors of AT corresponding to 1 = 0. 3. A and A' have three eigenvalues each, but 1 = 0 makes up two of the three since it corresponds to two linearly independent eigenvectors for both matrices. Find the third eigenvalue of A and A' by looking at the trace of A. 4. Show that (a, b, c) is the corresponding eigenvector of A and that (1, 1, 1) is the corresponding eigenvector of A' .
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