Math 205b Quiz 07 - Real Analysis, Bates College, 2009
ADVERTISEMENT
1Quiz 07 page 1
11/20/2009
Math 205B
Name
7
1
15
x
1. Let v
=
5
, v
=
, and v
=
3
. Also, let b =
7
.
y
1
2
3
2
x
4
4
1A. Find x and y such that S = {v
} form an orthogonal set.
, v
, v
1
2
3
1B. Find a unit vector in the direction of v
.
1
3
1C. Using the fact that the set S is an orthogonal basis of R
, use dot products to find the weight of v
when b is written
2
as a linear combination of {v
}. Show all your work.
, v
, v
1
2
3
3
9 6 12
1
4 2
5
2. Let Q =
.
2
7 4
9
3 11 6 14
2A. Find a basis B
for Col(Q).
1
⊥
2B. Find a basis B
for Col(Q)
.
2
2C. Verify that each member of B
is perpendicular to each member of B
.
1
2
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education