8.5WebPage - YIYAO LIU Math 308, section E, Fall 2014...

Current Score :
– / 22 Due : Friday, December 5 2014 10:00 PM PST
1. –/2 pointsHoltLinAlg1 8.5.001.
Find the vector in the subspace S closest to y
[-7/2; 7/2]
8
1
− 1
.
is
UW Common Math 308 Section 8.5 (Homework)
YIYAO LIU
Math 308, section E, Fall 2014
Instructor: Richard Balka
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y = , S = span
1
.
.

2. –/3 pointsHoltLinAlg1 8.5.003.
Find the vector in the subspace S closest to y .
[20/21; -37/21; 52/21]
Solution or Explanation
An orthonormal basis for S is given by and
The vector in S closest to y is
y = , S = span ,
1
− 1
3
1
2
− 3
5
− 1
1
v
1
= / =
1
2
− 3
1
2
− 3
−
1
14
14
1
7
14
3
14
14
v
2
= / = .
5
− 1
1
5
− 1
1
−
5
9
3
1
9
3
1
9
3
proj
s
y = ( v
1
·
y ) v
1
+ ( v
2
·
y ) v
2
=
·
+
·
=
.
−
1
14
14
1
7
14
3
14
14
1
− 1
3
−
1
14
14
1
7
14
3
14
14
−
5
9
3
1
9
3
1
9
3
1
− 1
3
−
5
9
3
1
9
3
1
9
3
−
20
21
37
21
52
21

3. –/2 pointsHoltLinAlg1 8.5.005.
Find the normal equations for the given system.
[69; -1]
The normal equations, are thus given by
3 x
1
− x
2
=
x
1
+
3 x
2
=
5 x
1
−
x
2
=
=
35 − 5
− 5 11
x
1
x
2
or
8
5
8
= .
.
,
.