Help linear operator problem

Cyannaca

Let T: R^3 -> R^3 be a linear operator and
T(x;y;z)= (x -y + 3z;2x-y+8z;3x -5y+5z).

Find the rule, for the linear operator S: R^3 -> R^3 such that ker S= Im T and Im S=Ker T.

I'm not really sure how I should start this problem. Also I would like to know if I can assume S is the inverse operator of T.

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Hurkyl

Staff Emeritus
Gold Member
Seems obvious to me that the first thing to do is to find ker T and im T. *shrug*

Also I would like to know if I can assume S is the inverse operator of T.
What do you think?

HallsofIvy

Homework Helper
" Also I would like to know if I can assume S is the inverse operator of T."

If the two kernals are not trivial, then T does not HAVE an inverse!

Cyannaca

I found ker T and Im T and I'm still stuck. I know it's not the inverse operator but I still don't know how to find the rule for the linear operator S.

Hurkyl

Staff Emeritus
Gold Member
Maybe if you described them geometrically, it would spark an idea?

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