3 X1 = ,X2 = -2 , X3 = 2 be eigenvectors of the matrix A which correspond to the eigenvalues 11 = -3, 12 = 0, and 13 = 4, respectively, and let X = 4 Express x as a linear combination of x1, X2, and x3, and find Ax. X = X1+ X2+ X3 . Ax =

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 16EQ
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3
X1 =
2
,X2 =
-2 , X3 =
2
be eigenvectors of the matrix A which correspond to the eigenvalues 11 = -3, 12 = 0, and 13 = 4, respectively, and let
X =
4
Express x as a linear combination of x1, X2, and x3, and find Ax.
X =
X1+
X2+
X3 .
Ах —
Transcribed Image Text:3 X1 = 2 ,X2 = -2 , X3 = 2 be eigenvectors of the matrix A which correspond to the eigenvalues 11 = -3, 12 = 0, and 13 = 4, respectively, and let X = 4 Express x as a linear combination of x1, X2, and x3, and find Ax. X = X1+ X2+ X3 . Ах —
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