# Vector spaces

1. Oct 16, 2004

### gunnar

I have :
c1(t+1) + c2(t^2 + 2) + c3(t^2 -t) = 0 for all t.
by specifying different values of t. I get
t=-1: 3c2 + 2c3=0
t=0: c1+2c2 =0
t=1:2c1 + 3c2 =0

How can I check that the only solution is c1=c2=cc3=0 ?

2. Oct 16, 2004

### arildno

Simply solve the system of equations you've just made for c1,c2,c3.

3. Oct 16, 2004

### gunnar

that's the problem I don't know how. I know it's simple but I just can't figure it out?

4. Oct 16, 2004

### arildno

You have 3 equations in 3 unknowns; you've seen that before?

5. Oct 16, 2004

### gunnar

I've done this when I have a matrix in reduce or reduce echelon but then I only have x1 in one linem here I have c1 in 2nd and 3rd row and it's there I am stuck. I admit I'm not very good at this. If you possibly can would you be so kind to lead my on with this problem??

6. Oct 16, 2004

### arildno

Why don't you just interchange line 1 and line 3?
Interchanging "topmost equation" with "bottom-most equation" can't possibly change the solution, or what?

7. Oct 16, 2004

### gunnar

I got it. Thanks a lot