Span of vectors

  • Thread starter physicsss
  • Start date
  • #1
319
0

Main Question or Discussion Point

I'm stuck on the following problem:

Describe the span of the vectors u1 and u2 in R^3, where
u1 = (1, 1, 1), u2 = (1, −1, 1)

I know that the span is a(u1)+b(u2), which becomes (a+b,a-b,a+b), but I don't know where to go from here.

TIA.
 

Answers and Replies

  • #2
mathwonk
Science Advisor
Homework Helper
10,963
1,137
do you know gaussian elimination, reduction for matrices?

i.e. how to solve for all vectors perpendicular to both of those?

or you could just look at your general vector, since it satisfies an obvious equation.
 
  • #3
lurflurf
Homework Helper
2,432
132
physicsss said:
I'm stuck on the following problem:

Describe the span of the vectors u1 and u2 in R^3, where
u1 = (1, 1, 1), u2 = (1, −1, 1)

I know that the span is a(u1)+b(u2), which becomes (a+b,a-b,a+b), but I don't know where to go from here.

TIA.
Consider (1/2)(u1-u2)=(0,1,0) and (1/2)(u1+u2)=(1,0,1)
It will then be easier to see what is happening.
 
  • #4
319
0
Is it the x-z plane in R^3?
 
  • #5
mathwonk
Science Advisor
Homework Helper
10,963
1,137
have you noticed that the first and third entries of your vectors are equal? what does that tell you about an equations characterizing these vectors?
 
  • #6
319
0
The main diagonal line in x-z plane
 
  • #7
mathwonk
Science Advisor
Homework Helper
10,963
1,137
i.e. x=z describes all of these vectors.
 

Related Threads on Span of vectors

  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
570
  • Last Post
Replies
21
Views
2K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
4
Views
2K
Replies
8
Views
13K
Replies
7
Views
758
  • Last Post
Replies
1
Views
3K
Top