the set of linear transformations. Let S={T:$\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$:T is a linear
transformation with T(1,0,1)=(1,2,3), T(1,2,3)=(1,0,1)} .Then S is 
(a) A Singleton Set 
(b) A finite set containing more than one element
(c) A countable set
(d) An uncountable set
MY APPROACH: 
T(1,0,1)=(1,2,3)$\Longrightarrow$T(e$^{1}+e^{3})$=(e$^{1}+2e^{2}+3e^{3})$
$\Longrightarrow$T(e$^{1})$+ T(e$^{3})$=e$^{1}+2e^{2}+3e^{3}Similarly,$T(e$^{1})$+2T(e$^{2})$+3T(e$^{3})$=e$^{1}$+e$^{3}$
I cant think more than this

Hint/Solution: A linear transformation is determined by its values on a basis,hence $S$ is uncountable.(Of course you need to fill some details)
