Ok I understand the definitions but am still struggling to decide if T is injective or not, for the kernel(T) obviously we know this equals the null space(T) so if I find one vector in R4 such that Tv=the zero vector does this mean it is injective.
eg. if I choose the vector
EDIT: by the way, for
Now, how can one show that ? Well, the only thing we have to do is solve for . Let .
hence is injective.