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^{2}->R

^{3}be given by T(x,y)=(x-y,2y-2x,0)

write down bases for its image and null-space and determine its rank and nullity.

Find the matrix A that represents T with respect to the standard bases of R

^{2}and R

^{3}

now i think i know how to do this but i'm revising and have no answers and would hate to be revising the wrong things, so can i please have a moment of someones time to confirm this is right, thanks

firstly A= {(1,-1),(-2,2),(0,0)}

kernal is when y=x so bases for a kernal is a(1,1) and n(t)=1

image is b(1,-2,0) r(t)=1

so r(t)+n(t)=2 as expected