Question

Help....too much math today. Show that the collection of all ordered 3-tuples (x1, x2, x3) whose components satisfy 3x1-x2+5x3=0 forms a vector space with respect to the usual operations of R3...don't really need an answer as much as I need someone to shed light on the problem :)

Answer 1

I think you may need to go through and show that it satisfies each axiom for being a vector space in Rn

Answer 2

closed under addition, closed under scalar multiplication, commutative addition, that a zero vector exists, etc

Answer 3

we are oinly given one vector though, where the axioms talk about having 2 vectors and adding them and such

Answer 4

you can make 2 arbitrary vectors <a, b, c> and <e, d, f>

Answer 5

oh ok thanks

Answer 6

then proceed through it.
i.e.
if both satisfy the equation, then
3(a+e) - (b+d) + 5(c + f) = 0

Answer 7

and do that sort of process with all the axioms

Answer 8

ok cool, I get it now