I have been stuck on a problem for awhile now and am in need of some help

Let be defined by . Let be th standard ordered basis for and = {(1,1,0),(0,1,1),(2,2,3)}. Compute .

Based on the answer in the back of the book it's supposed to be:

I have absolutely no idea how they got that solution, since when I input the values of the standard ordered basis I get .