SOLUTION: show that the linear transformation T defined by T(x1,x2)=(-2x1+x2,3x1,3x2+1)is not linear. Wow I am stuck. I have I have x1=(-2,3,0)+x2=(1,0,3)+(0,0,1) but I have know idea wher

Algebra ->  College  -> Linear Algebra -> SOLUTION: show that the linear transformation T defined by T(x1,x2)=(-2x1+x2,3x1,3x2+1)is not linear. Wow I am stuck. I have I have x1=(-2,3,0)+x2=(1,0,3)+(0,0,1) but I have know idea wher      Log On


   

Question 19367: show that the linear transformation T defined by T(x1,x2)=(-2x1+x2,3x1,3x2+1)is not linear. Wow I am stuck. I have I have x1=(-2,3,0)+x2=(1,0,3)+(0,0,1) but I have know idea where to go from here. I know that to be linear T(u+v)=T(u)+T(v)and T(cu)=cT(u) but I don't know how to show it. If someone could give me a hand I would REALLY appreciate it.
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Given T(x1,x2)=(-2x1+x2,3x1,3x2+1)is not linear.
What was that x1=(-2,3,0)+x2=(1,0,3)+(0,0,1) ????
If T is linear then T(0,0) = (0,0,0) , Now what is T(0,0) ?
Kenny