Finding transformation matrix of two bases

Hey guys,

i tried to figure out a solution for the following

**excercise:**

May B=(b1,b2) an ordered basis of the real vector space V and C=(c1,c2,c3) may be an ordered basis of the real vector space W. The map f:V→W is defined as

f(b1) = c1 + c2 + 2c3 and f(b2) = 2c1 + c2 - c3.

Find the matrix that transforms B to C of f.

**Idea:**

X * B = C

Since B is a 2x1 and C is a 3x1 matrix

X is supposed to be a 3x2 matrix to transform B to C. Is that right?

If yes, how to solve this equation system in which i have 6 unknows?

Thanks in advance!

Cheers,

Inf