Let A 0 1 2 01 2 Find dimensions of the kernel and image of

Let A = [0 -1 -2 0-1 -2] Find dimensions of the kernel and image of A (or the linear transformation T(x) = Ax). dim(Ker(A)) = dim(Im(A)) =

Solution

Second and third columns are identical

So col(A) is spanned by third column hencd dim(Col(A))=dim(Im(A))=1

By rank nullity theomre

dim(Im(A))+dim(ker(A))=3

So, dim(ker(A))=2