# 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.

Related Introductory Physics Homework Help News on Phys.org

#### 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?

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving