Let
and
a) Describe the linear subspace W {\displaystyle {}W} of the space of all 3 × 3 {\displaystyle {}3\times 3} -matrices that map the linear subspace U {\displaystyle {}U} into the linear subspace T {\displaystyle {}T} , as a solution space of a linear system.
b) Describe W {\displaystyle {}W} by an eliminated linear system.
c) Determine the dimension of W {\displaystyle {}W} .