Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: 1 = 1 with eigenvector v = and generalized eigenvector w= Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: t = c1 C2 e B. In fundamental matrix form: x(t)] C. As two equations: (write "c1" and "c2" for c and c2 ) x(t) = y(t) =

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 the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: (see image)

Write the solution to the linear system in the following forms:

A.  In eigenvalue/eigenvector form

B. In fundamental matrix form:

C.  As two equations: (write "c1" and "c2" for c1 and c2 )

Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector:
2 = 1 with eigenvector v =
4
and generalized eigenvector w =
Write the solution to the linear system r' = Ar in the following forms.
A. In eigenvalue/eigenvector form:
x(t)
t
= C1
y(t).
e
e
B. In fundamental matrix form:
x(t)
C1
y(t).
C. As two equations: (write "c1" and "c2" for cq and c2)
x(t) =
y(t) =
Transcribed Image Text:Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: 2 = 1 with eigenvector v = 4 and generalized eigenvector w = Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: x(t) t = C1 y(t). e e B. In fundamental matrix form: x(t) C1 y(t). C. As two equations: (write "c1" and "c2" for cq and c2) x(t) = y(t) =
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