We have the vectors a1 = (-2,5) and a2 = (-3,8) in the vector space R^{2 }and the linear transformation f: R^{2}-> R^{2}defined by

f(a1) = 2a1 - a2 and f(a2) = -4a1 + 2a2

I have to find the transformation matrix with respect to the standard basis for R^{2}.

My attempt :

It would be nice if someone could look at it