Suppose a matrix B has eigenvalues A = 2 and X2 = -2 with associated eigenvectors and x, = 1 5) respectively. The matrices P and D such that D = P-'BP are given by 2 and P = 2. (B) D = (1 2 1 (A) D = (. 1 -2 and P = 0 -2 -2 0 2 -2 -2 0 (C) None of the options apply (D) D = and P = 2 (E) D = and P = 0 -2 -2

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
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40. Suppose a matrix B has eigenvalues A = 2 and X2 = -2 with associated eigenvectors
%3D
and x, =
respectively. The matrices P and D such that D = P-'BP
are given by
2
and P =
1 2
1
(A) D =
(B) D =
and P =
-2 0
1 -2
2 -2
(C) None of the options apply
-2
(D) D =
and P:
2
(E) D =
and P =
0 -2
%3D
1 -2
Transcribed Image Text:40. Suppose a matrix B has eigenvalues A = 2 and X2 = -2 with associated eigenvectors %3D and x, = respectively. The matrices P and D such that D = P-'BP are given by 2 and P = 1 2 1 (A) D = (B) D = and P = -2 0 1 -2 2 -2 (C) None of the options apply -2 (D) D = and P: 2 (E) D = and P = 0 -2 %3D 1 -2
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