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Unformatted text preview: The fundamental matrix for the system
x x is given by Direct multiplication results in
page 408 —————————————————————————— CHAPTER 7. —— Hence 15 . Let be arbitrary, but fixed, and variable. Similar to the argument in Prob. ,
the columns of the matrix
are linear combinations of fundamental solutions.
Hence the columns of
are also solution of the system of equations. Further,
is a solution of the
initial value problem Z
AZ , with Z
Now consider the change of
. Let W
. The given initial value problem can be
that AW , with W is a fundamental matrix satisfying A , with I , it follows W
. Based on Part W Z . , I . Hence . It also follows that
16. Let A be a diagonal matrix, with A
positive integer, ,
A e e
e e e
e . Note that for any . It follows, from basic matrix algebra, that ____________________________________...
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This note was uploaded on 03/11/2014 for the course MA 303 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.
- Spring '08