4. (*) Let L: V → V be a linear transformation. b) Suppose that L is invertible, that U is an L-invariant subspace of V. For any v U, show that L(v) & U. c) If V has dimension n and U is an L-invariant subspace of dimension m, prove that there is a basis B for V so that the matrix of L with respect to B has the following shape: 0 0 a1,1 a1,m : 0 0 am,1 am,m [L]B = b1,1 b1,m C1,1 C1,n-m bn-m,1 bn-m,m Cn-m,1 Cn-m,n-m

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A: Solve the following problem

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