Linear equation, span, vectors, linear systems of equations

[tk1234]

show that S and T have the same span in R^3 by showing that the vectors in S are in the span of T and vise versa.

S= {(1,0,0), (0,1,0)}
T= {(1,2,0), (2,1,0)}im a little confused on how to start off on this problem.. help?!

 

[Dick]

Well, basically you just do what they suggested. For example, how would you show (1,2,0) is in the span of (1,0,0) and (0,1,0)?

 

[tk1234]

thats what I am confused about.. how would i start it off..?

 

[brugel]

An example of how to show (1,2,0) is in the span of {(1,0,0),(0,1,0)}
a(1,0,0) + b(0,1,0) = (1,2,0) where a = 1, b = 2

this might help you also
http://www.khanacademy.org/video/linear-combinations-and-span?playlist=Linear Algebra

 

[tk1234]

okay. i get it. haha... it was actually easy.. i was just a little confuse :) thanks!