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Math 20F  Linear Algebra  Winter 2003
Quiz #
6
1
2
Answers — March 4
1. Consider the following table of data values.
x
1
0
1
2
y
0424
Find the best linear least squares ﬁt to the data. That is, ﬁnd the linear
function
f
(
x
)=
c
0
+
c
1
x
that best ﬁts the data in the least squares
sense.
ANSWER: Let
A
=
1

1
10
11
12
and
b
=
0
4
2
4
.
We need to solve
A
‡
c
0
c
1
·
=
b
.
To do this, we solve
A
T
A
x
=
A
T
b
.N
o
w
,
A
T
A
=
±
42
26
¶
, and
A
T
b
=
(
10
10
)
, so we use row operations:
±
10
10
¶
→
±
21
5
13
5
¶
→
±
5
5
¶
→
±
5
0

5

5
¶
Solving by backsubstitution gives
c
1
=1
and
c
0
=2
. So the answer is:
f
(
x
)=2+
x
.
2. Let
u
1
=(1
,
1
,
1)
T
and
u
2
,

1
,
0)
T
. Are these vectors orthogonal?
Orthonormal? Let
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 Winter '03
 BUSS
 Linear Algebra, Algebra, Least Squares

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