A is a 2X2 matrices.T is a transformation from
T differs zero. T is not isomorphism
prove that dim ImT=dim KerT=2
if T differs zero then its representative matrices A differs zero too.
because T is not isomorphism then its singular so we have only one row
of seros in A.
so rank(A)=1 and null(A)=1
so there is only one k 2X2 matrices which sends for which T(k)=0
the solution in my book says that this k matrices is a tranposed
vector (a,b)
??
why??
our result has to be 2x2 matrices
whith
transposed (a,b) we cant get 2x2 matrices
?