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real vector space with subspaces

Source: IMC 1998 day 1 problem 1

October 22, 2005
vectorlinear algebralinear algebra unsolved

Problem Statement

Let VV be a 10-dimensional real vector space and U1,U2U_1,U_2 two linear subspaces such that U1⊆U2,dim⁡U1=3,dim⁡U2=6U_1 \subseteq U_2, \dim U_1 =3, \dim U_2=6. Let ε\varepsilon be the set of all linear maps T:V→VT: V\rightarrow V which have T(U1)⊆U1,T(U2)⊆U2T(U_1)\subseteq U_1, T(U_2)\subseteq U_2. Calculate the dimension of ε\varepsilon. (again, all as real vector spaces)
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