Let T: be a linear transformation - Math

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Let T: be a linear transformation so thatT(x,y,z)=(x+y,y-z). Find a basis for kerT and imT.

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Look at the matrix corresponding to this transformation:
which is already in reduced echelon form.The image space
is the same as the columnspace of A, so given by the pivot columnsof A, the first two columns,
so all of can be reached. You can choose thestandard basis.
The kernel is the same as Nul(A). We see that
, so a basis for the nulspace is thesingle vector