Linear transformation

[stud]

I need help with question from homework in linear algebra.

 

This question (linear transformation):

http://i43.tinypic.com/15reiic.gif

 

According to theorem dimensions:

dim(V) = dim(Ker(T)) + dim(Im(T)).

 

dim(Ker(T))=2.

dim(V) in R^4, meaning =4.

 

We can therefore conclude that dim(Im(T))=2.

But how can find this specific linear transformation?

 

Please help me to solve this problem.

Thanks.

Edited January 16, 2012 by stud

[DrRocket]

I need help with question from homework in linear algebra.

 

This question (linear transformation):

http://i43.tinypic.com/15reiic.gif

 

According to theorem dimensions:

dim(V) = dim(Ker(T)) + dim(Im(T)).

 

dim(Ker(T))=2.

dim(V) in R^4, meaning =4.

 

We can therefore conclude that dim(Im(T))=2.

But how can find this specific linear transformation?

 

Please help me to solve this problem.

Thanks.

 

You can't, nor does the problem ask you to.

 

You are given two vectors in the kernel of T. That does not define T uniquely.

 

You are only asked to find some transformation with the specified kernel, not any specific one. There are, in fact, infinitely many solutions to your problem.

[stud]

Can you please guide me to solve? I can not figure out how to solve it.

Thx.

[DrRocket]

Can you please guide me to solve? I can not figure out how to solve it.

Thx.

 

You need to show what you have done and some reasonable attempt. We won't do your homework for you.