How do we find scalar coefficients for a linear combination in linear algebra?

[roam]

Hello!
I have just started studying linear algebra and I got the following question:

We have:
http://img528.imageshack.us/img528/7687/dfdsf1lj3.gif

Expres u as a linear combination of the vectors v and w.







This is my attempt;
(By definition a vector is called a linear combination of $$v_{1}, v_{2},... v_{k}$$ if it can be expressed in form $$c_{1}v_{1}, c_{2}v_{2},... c_{k}v_{k}$$ )

So we get: $$c_{1} (4,3,2,1) + c_{2} (1,1,1,1)$$

Is this right? Is this all we were required to show?

Thanks you.

 

[Hootenanny]

You would also need to determine the values of the scalar coefficients.

 

[roam]

How do we find the values of the scalar coefficients i.e., $$c_{1} , c_{2}$$? Thant's my problem...

Thanks.

 

[Hootenanny]

How do we find the values of the scalar coefficients i.e., $$c_{1} , c_{2}$$? Thant's my problem...

Thanks.

Well, you have two unknowns which must satsify a system of four equations. Solve.