Question

I am confused, please explain me. \[R^2\text { is a subspace of }~R^3 \]??

Answer 1

@dan815

Answer 2

any line that passes through the origin is a subspace of r3

Answer 3

I am with you but the book says no. that's why.

Answer 4

not all r2 is

Answer 5

only the lines that pass through the origin

Answer 6

only if the line has has a linear combination that equal 0 without the linear combination coefficient being 0

Answer 7

so, the subspace of R^2 which contains all of lines through origin is a subspace of R^3, not the whole R^2, right?

Answer 8

yes

Answer 9

ok, thanks a lot, friend

Answer 10

because if you have a line in r3 that doesnt pass trhough the origin then yhou can have a linear combination that leaves the origin, or just multplying by zero u know u are not on that r2 space anymore

Answer 11

there is no subspace that exists without containting the origin

Answer 12

one more question, dan?

Answer 13

okay i will asnwer after ,i have to go pick up my brother

Answer 14

I am waiting until then to ask, signal me then,ok?

Answer 15

oh and umm r2 is a plane i mean a plane that passes throug hte origin!! okay brb

Answer 16

if m<n, then any spanning set of R^n must contain more vectors than any spanning set for R^m, true, false?

Answer 17

try to vizualize it u can do it

Answer 18

if u mean linearly dependant vectors then false but not linearly dependant u can have infinite vectors but they will be redundant

Answer 19

for example to define a point in r2 space a plane if you use 2 well defined vectors that are orthogonal, u can go through any point in that r2 space but, u can also go throught that point with 3 vectors or addition of 4 vectors and so on..