Question

Let v1,v2,v3 be a list of vectors in R^2. Does it necessarily hold that span(v1,v2,v3) = R^2

Answer 1

(1,0),(2,0),(3,0)

Answer 2

so to prove my answer, it would be enough to give a specific example such as the one above?

Answer 3

to disprove all you need is a counter example

Answer 4

okay, so (1,0) (2,0) (3,0) is a counter-example? why?

Answer 5

what is the span of those 3 vectors

Answer 6

can you take a linear combination of those 3 vectors and get (1,1)?

Answer 7

Sorry, I was working through the calculations. Nope, because you would get two equations: a1+ 2a2 +3a3 = 1 and 1= 0 (which is never true). Thanks! @Zarkon