Question

does this vectors span R^3 and why not?
cmon people help me, i have helped sooo many of you but i never get my questions answered,

Answer 1

\[\left(\begin{matrix}1 \\ 4\\5\end{matrix}\right),\left(\begin{matrix}5 \\ 9\\2\end{matrix}\right)\]

Answer 2

youve never answered any of my questions; so does that mean i shouldnt help you?

Answer 3

what does it mean to span R^3?

Answer 4

if span means that it can create every vector in R^3; then no. 2 vectors define a plane that is a subspace of R^3 assuming that the 0 vector is part of that plane

Answer 5

well i typed this question 3-4 times, i had to say something to get someone to answer my question,

everyone goes to people whom ask easy questions or that have a picture of the oposite sex,

so when i ask my questions...
i have to ask in a sympathetic way or put a picture of a person to attract others


PS thanks i understand now,


but will V1, V2, V3, V4, all 3 by 1 vectors span R^3?

Answer 6

you had to get the right people to notice your question is all; im sure you dont want the people who are drawn in by a fictitious portrayal to handle this sort of thing do you?

Answer 7

im still having difficulty recalling a proper definition for span, can you refresh em memory?

Answer 8

v1, v2, v3, v4 may or maynot form a basis in R^3 even tho their components are 3x1

Answer 9

i understand, but the right people are not many.


here is a picture of the definition, i dont understand it though,

Answer 10

W is just a collection of vectors that can be used within the space of W

if R^3 is spose to represent W, then in order to span R^3 we would need a collection of vectors that are at least able to be constructed from:\[\begin{pmatrix}1\\0\\0\end{pmatrix},\begin{pmatrix}0\\1\\0\end{pmatrix},~and~\begin{pmatrix}0\\0\\1\end{pmatrix}\]

Answer 11

theres a book upstairs that id have to reread to be sure that im not confusing things tho. I took linear algebra last semester and it feel like an eternity ago

Answer 12

lol, im doing it now and it feels the same way.

i understand what you said,
it makes sense, like you cannot represent a 3D space with only 2 vectors,

Answer 13

http://tutorial.math.lamar.edu/Classes/LinAlg/Span.aspx

example 5 looks like it can be useful

Answer 14

i have one more question to ask,

how can you find a basis to R^3 consisting of eigenvectors?

Answer 15

"The real question is whether or not R^3 will be contained in the span of these vectors"

Answer 16

eigens, really? hmmm

Answer 17

an eigene is what ...

(A-LI)x = 0 right?

Answer 18

yes, it is the x

i am doing a question to which i have found all eigen vectors, [1 repeating eigen value], so do i just do [v1,v2,v3] then find if they are independent by doing [v1,v2,v3][c1 c2 c3] =0, to see if c1=c2=c3=0?

would that be sufficient because obviously it will span R^3

Answer 19

if the eigene vectors are linearly independant; then they would have to span R^3

Answer 20

what are the specifics of the problem?

Answer 21

the problem was to find a basis consisting of eigenvectors of a matrix 3x3

can we find a basis?

Answer 22

we can find a eigenespace ... but its not really guaranteed that the space will span R^3

Answer 23

no worries, i think i need to go through some books again.

Thank you very much for your help, i have since gained more faith in this community after you have answered my question.

thank you,

Rezz

Answer 24

good bye

Answer 25

good luck ;)