Math 205a,b - Linear Algebra Worksheet - 2013
ADVERTISEMENT
1MATH 205A,B - LINEAR ALGEBRA
WINTER 2013
QUIZ 9
NAME:
Section:(Circle one)
A(1 : 10)
B(2 : 40)
Show ALL your work CAREFULLY.
(a) Let
1
3
2
2
6
1
=
=
=
1
2
3
3
5
0
Determine whether the set
=
is an orthogonal set. Justify your answer.
1
2
3
The set
is orthogonal if and only if each of the following dot products
,
,
1
2
2
3
is zero. Since
= ( 1)(3)+(2)( 6)+(3)(5) = 0,
= (3)(2)+( 6)(1)+(5)(0) = 0,
3
1
1
2
2
3
and
= (2)( 1) + (1)(2) + (0)(3) = 0, we conclude that
is an orthogonal set.
3
1
4
1
2
1
(b) Let
=
and
=
. Find the projection of
onto
= Span
.
3
2
The projection of
onto
is given by
proj
=
(4)(1) + ( 2)( 1) + (3)(2)
=
2
2
2
1
+ ( 1)
+ 2
2
=
2
4
(c) Let
and
be as in part (b). Find the shortest distance between
and the line (through
origin)
.
The closest point in
to
is proj
so the shortest distance in question is the length
4
2
proj
=
2
2
=
5
3
4
Date: March 27, 2013.
1
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education