Confused with working out the span of a set of vectors in R^2

by gilabert1985
Tags: confused, span, vectors, working
gilabert1985 is offline
Apr27-12, 04:30 AM
P: 7
Hi everyone!

I have the following problem which I don't understand... It is already solved, but there are three questions I have regarding it.

The problem says: "Let S be the set of all vectors [itex]x=(x_{1}, x_{2})[/itex] in [itex]\Re^{2}[/itex] such that [itex]x_{1}=1[/itex]. What is the span of S?"

And here is the answer that has me so confused...

"[itex]span S = \Re^{2}[/itex] because [itex](x_{1}, x_{2})=x_{1}(1, x^{-1}_{1}x_{2}[/itex] when [itex]x_{1}\neq0[/itex]
and [itex](x_{1}, x_{2})=(1, 0)-(1, -x_{2})[/itex] when [itex]x_{1}=0[/itex]."

But I don't understand the first line... why does it say when [itex]x_{1}\neq0[/itex] if [itex]x_{1}[/itex] is supposed to be equal to 1?

And in the second line, the same... why is [itex]x_{1}=0[/itex]?

So yeah, I understand they are linear combinations and all that, but for the condition given ([itex]x_{1}=1[/itex]), I don't understand how this answer satisfies it.
Phys.Org News Partner Science news on
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
Office_Shredder is offline
Apr27-12, 05:26 AM
P: 4,499
The points (x1,x2) in the lines that are confusing you are not points in S, but points in R2, which it then shows how to represent as linear combinations of points in S
Fredrik is offline
Apr27-12, 08:05 AM
Sci Advisor
PF Gold
Fredrik's Avatar
P: 9,012
Since you can't rewrite ##x_2## as ##x_1 x_1{}^{-1}x_2## when ##x_1=0##, you have to consider the case ##x_1=0## separately.

Register to reply

Related Discussions
span of vectors Calculus & Beyond Homework 2
How many vectors in span({v}) Calculus & Beyond Homework 6
span of two vectors Calculus & Beyond Homework 7
span of a set of 3D vectors Calculus & Beyond Homework 1
span of vectors Linear & Abstract Algebra 6