| Thread Closed |
span of vectors |
Share Thread | Thread Tools |
| Jun30-05, 04:30 AM | #1 |
|
|
span of vectors
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. |
| Jun30-05, 12:06 PM | #2 |
|
Recognitions:
|
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. |
| Jun30-05, 07:24 PM | #3 |
|
Recognitions:
|
It will then be easier to see what is happening. |
| Jun30-05, 09:55 PM | #4 |
|
|
span of vectors
Is it the x-z plane in R^3?
|
| Jun30-05, 09:58 PM | #5 |
|
Recognitions:
|
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?
|
| Jun30-05, 10:10 PM | #6 |
|
|
The main diagonal line in x-z plane
|
| Jun30-05, 11:05 PM | #7 |
|
Recognitions:
|
i.e. x=z describes all of these vectors.
|
| Thread Closed |
| Thread Tools | |
Similar Threads for: span of vectors
|
||||
| Thread | Forum | Replies | ||
| The dimension of the span of three linearly independent R^3 vectors | Calculus & Beyond Homework | 6 | ||
| span of two vectors | Calculus & Beyond Homework | 7 | ||
| LINEAR ALGEBRA: Find vectors that span the image of A... | Calculus & Beyond Homework | 3 | ||
| span of a set of 3D vectors | Calculus & Beyond Homework | 1 | ||
| Prove span(S1 U S2) = span(S1) + span(S2) | Calculus & Beyond Homework | 10 | ||