Finding transformation matrix of two bases
i tried to figure out a solution for the following
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.
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!