Math 252 — Fall 2002
Answers to Matrix Exponential Exercises
Answers, using Maple (you should do the problems by hand, but it is useful to know how to check your
answers using Maple):
First introduce a package that understands matrices. The new
LinearAlgebra
package is used to
exploit its more natural (if somewhat verbose) set of function names. Once the package is loaded, the matrices
appearing in the exercises can be defined. Since the matrices are small, it is equally easy to enter them by
rows or by columns. A mixture of both styles is used to illustrate the use of these
shortcuts
for defining
matrices. Almost all matrices are called
A
in the problem statements, so we do the same here, modified by
information about the source of the problem. Note that we ask Maple to find
A
+
B
in problem 5.
with(LinearAlgebra):
A1a := < <1  1>,<0  0> >;
A1b := < <5,1>  <6,2> >;
A1c := < <2,1>  <8,4> >;
A1d := < <2,0,0>  <2,1,0>  <1,2,1> >;
A4 := < <0,0,0>  <1,0,0>  <2,1,0> >;
c5 := <1,0>; A5 := <c5  c5>;
B5 := ZeroMatrix(2,compact=false); B5[1,2] := 1;
AplusB5 := A5 + B5;
Here is the response
A
1
a
:
=
1
1
0
0
A
1
b
:
=
5
6

1

2
A
1
c
:
=
2

8
1

4
A
1
d
:
=
"
2
2
1
0
1
2
0
0

1
#
A
4 :
=
"
0
1
2
0
0
1
0
0
0
#
c
5 :
=
1
0
A
5 :
=
1
1
0
0
B
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 Spring '08
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 Matrices, 1 Aplus B5, Matrix Exponential Exercises

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