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Thursday section time:
Student ID:
Math 20F  Linear Algebra  Spring 2003
Answers to Selfassessment Quiz #5.5 — May 22
You must show your work in order to get credit for a problem.
Label your answers clearly.
1.
Let
u
1
= (1
,
1
,
1
,
0)
T
and
u
2
= (0
,
1
,
1
,
1)
T
.
Let
U
=
Span
(
u
1
,
u
2
).
Find a basis for
U
⊥
.
ANSWER: Form the matrix
A
=
1
1
1
0
0
1
1
1
¶
. The nullspace of the
matrix is equal to
U
⊥
, since
R
(
A
T
) =
U
. After finding also solutions
to
A
x
=
0
(details of work omitted), we have
U
⊥
=
Span
((1
,

1
,
0
,
1)
T
,
(0
,
1
,

1
,
0)
T
)
.
2
Find the linear function that best approximates data
x
2
0
1
2
y
2
0
1
2
in the least squares sense.
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 Spring '03
 BUSS
 Linear Algebra, Algebra, u2, Thursday section time, best approximates data

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