Hello,

I'm trying to figure out if (m-1)vectors of R^m can generate R^(m-1)?

What I've tried to do so far is this:

Let's take u_1,u_2,u_3 element of R^4 (with m=4)

By definition (I think)

u = sum(lambda_i*u_i,k=1,k=n)

I suppose u = (x,y,z) element of R^3 (m-1), u_1=(1,0,0,0), u_2=(0,1,0,0), u_3=(0,0,1,0)

A=[u_1 u_2 u_3]=

1 0 0

0 1 0

0 0 1

0 0 0

We know A*lamda_matrix=u

[ 1 0 0 ][lambda_1]=[lambda_1]=?? [x]

[ 0 1 0 ][lambda_2] [lambda_2] [y]

[ 0 0 1 ][lambda_3] [lambda_3] [z]

[ 0 0 0 ]...............=.. [0]

(4x3 * 3x1 = 4x1)

(I used ..... so the [0] wouldn't go in the multiplication, forum escapes whitespace)

So can I say that (lambda_1,lambda_2,lambda_3,0)=(x,y,z)? I would doubt so...

If (m-1) vectors from R^m can generate R^(m-1) I would like a proof and if not a counter-example.

Is it the right way to go with this or should I use something else?

Thanks (: