2. Suppose that you are told the matrix c – 26 с 2b — а A = 36 —а — 26 + 2с b а+2b [3 2 1]". has an eigenvalue of 6 with corresponding eigenvector v = (i) Determine the values of a, b, and c. 6, and A3 = 3. Find an eigenvector of w of (ii) corresponding to the eigenvalue X3 = 3. The eigenvalues of A are A1 = \2

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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2. Suppose that you are told the matrix
b c- 26
с 2b — а
a
A
3b
26 + 2c b
a + 26
has an eigenvalue of 6 with corresponding eigenvector v = 3
2 1]".
(i)
Determine the values of a, b, and c.
(ii)
corresponding to the eigenvalue A3 = 3.
The eigenvalues of A are A1
12 = 6, and d3
3. Find an eigenvector of w of A
Transcribed Image Text:2. Suppose that you are told the matrix b c- 26 с 2b — а a A 3b 26 + 2c b a + 26 has an eigenvalue of 6 with corresponding eigenvector v = 3 2 1]". (i) Determine the values of a, b, and c. (ii) corresponding to the eigenvalue A3 = 3. The eigenvalues of A are A1 12 = 6, and d3 3. Find an eigenvector of w of A
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