Spring 2009 – Math 33 Name:
Quiz #8 Take-Home (due Wednesday, 3/18/09)
Use your own paper and staple this sheet on top of your work papers. Make sure
your work papers are in order and numbered clearly.
1. (3 pts.) Determine the matrix representation
[
]
C
B
T
for the linear transformation
T
and the ordered bases
B
and
C
:
2 3
:
T P P
→
,
(
)
(
)
(
)
(
)
1
T p x x p x
= +
( )
{
}
2
1, 1, 1
B x x= + +
( ) ( )
{
}
2 3
1, 1, 1 , 1
C x x x= + + +
2. (3 pts.) Solve the system of differential equations:
1 1 2
2 3
x x x
′
= −
2 1 2
2
x x x
′
= −
3. (4 pts.) Determine an orthogonal matrix S such that
(
)
1 2
diag , , ,
T
n
S AS
λ λ λ
=
…
for
2 0 0
0 3 1
0 1 3
A
=