Show that the transformation T, T(x1,x2)=(4x1-2x2, 3|x2|) is not linear.
To show its not linear, either T(0) can not = 0, or T(u+v) cannot = T(u) + T(v).
Letting x1, x2 = 0, we get T(0)=0, so this doesn't prove its not linear.
Thus we need to show T(u+v) cannot = T(u) + T(v).
I'm not sure how to go about doing this though.
To show its not linear, either T(0) can not = 0, or T(u+v) cannot = T(u) + T(v).
Letting x1, x2 = 0, we get T(0)=0, so this doesn't prove its not linear.
Thus we need to show T(u+v) cannot = T(u) + T(v).
I'm not sure how to go about doing this though.