Thread: Lin transformation problem

Find linear transformations U, T: F^2 -> F^2 such that UT = T[0] (THE ZERO TRANSFORMATION) but TU doesnt equal T[0]. Use your answer to find matrices A and B such that AB = 0 but BA doesnt equal 0.

ANy1 kno this?

Originally Posted by ruprotein

Find linear transformations U, T: F^2 -> F^2 such that UT = T[0] (THE ZERO TRANSFORMATION) but TU doesnt equal T[0]. Use your answer to find matrices A and B such that AB = 0 but BA doesnt equal 0.

ANy1 kno this?

Let U: (x,y) -> (x,0), and T: (x,y) -> (0,x).

Then UT: (x,y) -> (0,0), and TU: (x,y) -> (0,x).

RonL