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

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Homework Help Overview

The discussion revolves around finding a basis for the image of a set S, specifically denoted as L(S). The context involves linear algebra concepts related to vector spaces and spans, particularly focusing on a plane defined by the equation x1 + 3x2 + x3 = 0.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss identifying two column vectors that span the plane S and question how to select points on the plane. There is an exploration of the relationship between the basis for S and the basis for L(S).

Discussion Status

Some participants have offered guidance on how to find a basis for the plane S, while others clarify the need to focus on L(S). The conversation reflects a mix of understanding and confusion regarding the distinction between S and L(S).

Contextual Notes

There is a reference to an image that contains additional information relevant to the problem, which may not be fully articulated in the text. Participants also acknowledge a misunderstanding in the initial explanation regarding the basis being sought.

murielg
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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 ?
 
Last edited by a moderator:
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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.
 
Last edited by a moderator:
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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