Suppose that you are told the matrix a C - 26 A = 36 с 2b — а -а — 2b + 2с b a+2b nas an eigenvalue of 6 with corresponding eigenvector v= [3 2 1]*. | Determine the values of a,b, and c. ii) to the eigenvalue 13= 3. ) The eigenvalues of A are 1, = 12 = 6, and A3 = 3. Find an eigenvector of w of A corresponding %3D

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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Suppose that you are told the matrix
с — 2Ь
2b – a
A =
3b
-а — 2b + 2с b
a + 26
[3 2 1]".
has an eigenvalue of 6 with corresponding eigenvector v =
| Determine the values of a,b, and c.
(i)
) The eigenvalues of A are 2, = 12 = 6, and 13 = 3. Find an eigenvector of w of A corresponding
(ii)
to the eigenvalue 23= 3.
Transcribed Image Text:Suppose that you are told the matrix с — 2Ь 2b – a A = 3b -а — 2b + 2с b a + 26 [3 2 1]". has an eigenvalue of 6 with corresponding eigenvector v = | Determine the values of a,b, and c. (i) ) The eigenvalues of A are 2, = 12 = 6, and 13 = 3. Find an eigenvector of w of A corresponding (ii) to the eigenvalue 23= 3.
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