Question

Define the span of a set of vectors and the basis of a set of vectors.

Answer 1

Well the span is basically all of the possible combinations of multiples of the vectors in the set.
So, a vector is in the span if it is possible to write it as a linear combinations of vectors in the set.

Answer 2

Quick example:
Set A = {(1, 0), (0,1)}
Is (15, -7) in the span of A? Well, I could write it as 15(1,0) -7(0,1), which is a linear combination of the vectors in A, so yes.

And in fact, it's possible to get any ( , ) vector this way, so the span of A is all of R2

Answer 3

Understand? Ask me questions.

Answer 4

Yeah, I just wanted to see how to define it. It was on my exam yesterday to define the span, the basis, and a few other things only in words (no symbols).

Answer 5

Ooooh, well. Hmm, do you know how rigorous of a definition your professor wants?

Answer 6

no idea. hopefully hes not a tough grader on it.

Answer 7

I mean, he might be looking for an "in your own words" intuitive definition, showing that you understand. Or he might want you to legit spew back the book definition at him haha

Answer 8

i did what i could. i'll find out monday.

Answer 9

That class was such a pain for me -_-

Answer 10

differential equations sucked for me. i still have another half for this class, different professor.

Answer 11

Yeah, weirdly for me, I wasn't very into the mid-level mathematics like linear or diffEQ, but when I got to Modern Algebra and Advanced Calc I loved it.

Answer 12

i don't have to take those, just modern geometry, number theory and history of math

Answer 13

Ah. College Geometry was fun for me. History is an extremely interesting course, and I found it to be a nice change of pace from my other math courses. I actually didn't have to take number theory, but I wish I had =/

Answer 14

you can take it for me haha

Answer 15

How kind of you! =D

Answer 16

Yes yes, I am so generous

Answer 17

<3