Homework Statement
Prove whether or not the following linear transformations are, in fact, linear. Find their kernel and range.
a) ## T : ℝ → ℝ^2, T(x) = (x,x)##
b) ##T : ℝ^3 → ℝ^2, T(x,y,z) = (y-x,z+y)##
c) ##T : ℝ^3 → ℝ^3, T(x,y,z) = (x^2, x, z-x) ##
d) ## T: C[a,b] → ℝ, T(f) = f(a)##
e) ##...