1. ## Spanning set.

A subspace of $\displaystyle \mathbb{R}^3$ is given by:
$\displaystyle S=\lbrace (a,b,c)|a-10b+12c=0 \rbrace$

Determine two vectors X and Y such that {X, Y} forms a spanning set for S.
-------------------------
Hmm...

Now I understand that I need to find two vectors such that set of all combinations:

$\displaystyle \lbrace aX + bY | a, b \in R \rbrace = S$
but I'm not sure how to proceed from here...

2. Originally Posted by scorpion007
A subspace of $\displaystyle \mathbb{R}^3$ is given by:
$\displaystyle S=\lbrace (a,b,c)|a-10b+12c=0 \rbrace$

Determine two vectors X and Y such that {X, Y} forms a spanning set for S.
-------------------------
Hmm...

Now I understand that I need to find two vectors such that set of all combinations:

$\displaystyle \lbrace aX + bY | a, b \in R \rbrace = S$
but I'm not sure how to proceed from here...
a- 10b+ 12c= 0 so a= 10b- 12c. Choose values for b and c and solve for a.

I recommend, because it is easy, b= 1, c= 0 for one vector, b= 0, c= 1 for the other.