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

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To find a basis for the subspace S defined by the plane equation x1 + 3x2 + x3 = 0, two linearly independent vectors v1 and v2 that span the plane must be identified. The discussion clarifies that any two points on the plane can define a line, but to establish a basis, one must express the plane in terms of linear combinations of vectors. The transformation L(v1) and L(v2) is necessary to find the basis for the image L(S), not just S. The participants emphasize the importance of correctly interpreting the problem and ensuring clarity in communication. Understanding the distinction between S and L(S) is crucial for solving the homework problem effectively.
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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 ?
 
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murielg said:

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.
murielg said:
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.
murielg said:
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.
 
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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
 
Please reread my last reply...
 
JUST DID! sorry i read it too fast the first time
THANK YOU! :)
 

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