Thread: dimention of kernel

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


?

Originally Posted by transgalactic

A is a 2X2 matrices. T is a transformation from T differs zero. T is not isomorphism prove that dim ImT=dim KerT=2

This is nonsense. What has to do in respect to ?

if T maps a 2x2 matrix to a 2x2 matrix, then a representative matrix for T is 4x4. it is not clear from your question what "A" is.