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Basis and Span

Yankel

Active member
Jan 27, 2012
398
Hello

A base of some space is a set of vectors which span the space, and are also linearly independent.

I am looking for an example of vectors which DO span some space, but are dependent and thus not a base...can anyone give me a simple example of such a case ?

thanks !
 

Jameson

Administrator
Staff member
Jan 26, 2012
4,043
The easiest way I can think of generalizing this is to start with a basis and then just add one more vector to the set which is a multiple of one of the other vectors.

For example, the vectors \(\displaystyle \left \{ (1,0),(0,1),(1,2) \right \}\) span $\mathbb{R}^2$ but this set isn't a basis.
 

Yankel

Active member
Jan 27, 2012
398
exactly what I was looking for, thanks !