Find a BASIS for L(S) -The Image of S

[murielg]

Homework Statement

[PLAIN]http://sphotos.ak.fbcdn.net/hphotos-ak-ash2/hs574.ash2/149609_293915114994_507054994_1176494_3477051_n.jpg

Homework Equations

The Attempt at a Solution

Ok so I know that this plane goes thru the origim
I guess to find the two column vectors that span S, say v1 and v2
so i need to find two points on that plane that are not in the same line, right?
and then do L(v1) and L(v2) to find the basis for S ?

 

[Mark44]

Homework Statement

[PLAIN]http://sphotos.ak.fbcdn.net/hphotos-ak-ash2/hs574.ash2/149609_293915114994_507054994_1176494_3477051_n.jpg

Homework Equations

The Attempt at a Solution

Ok so I know that this plane goes thru the origim
I guess to find the two column vectors that span S, say v1 and v2

The equation of the plane is x₁ + 3x₂ + x₃ = 0.
You can find a basis for the plane this way:
x₁ = -3x₂ - x₃
x₂ = x₂
x₃ = ...x₃
If you squint at that awhile, you might see that any vector in the plane is a linear combination of two vectors. Those vectors are your basis for S.

so i need to find two points on that plane that are not in the same line, right?

That's not possible. You can run a line through any two points on a plane.

and then do L(v1) and L(v2) to find the basis for S ?

No, calculate L(v1) and L(v2) to find a basis for L(S). You should already have a basis for S from the work above.

 

[murielg]

Thanks for your answer.
I need to find the basis for L(S) not just S
Sorry i made a mstake when writing my explanation, but it's rigth there in the image i attached.
Thanks

 

[Mark44]

Please reread my last reply...

 

[murielg]

JUST DID! sorry i read it too fast the first time
THANK YOU! :)