I am confused about L(u3) in this question.
Basis B = {u1=[1,1,1],u2=[1,1,0],u3=[1,0,0]} Let L(c1u1+c2u2+c3u3)=(c1+c2+c3)u1+(2c1+c3)u2-(2c2+c3)u3
Find the matrix of L with respect to B
L(u1)=L(1u1+0u2+0u3)= [1,2,0]
L(u2)=L(0u1+1u2+0u3)= [1,0,-2]
L(u3)=L(0u1+0u2+0u3)= [1,1,0]
This is all work that is given to me but shouldn't L(u3)=[1,1,-1]? I get L(u1) and L(u2) but L(u3) makes no sense. I get how the first two values are 1 but why is the third value in vector 0?