can you please help with question 11?
Let $T \in L(V,V).$ Extend Theorem (28.10) to prove that there exists a linear transformation $T^{(k)}$ of $\bigotimes_k(V)$ such that $$ T^{(k)}(v_1 \otimes \cdots \otimes v_k) = T(v_1) \otimes \cdots \otimes T(v_k) \quad \text{for all } v_i \in V. $$ Prove that $\bigwedge_k (V)$ is an invariant subspace relative to $T^{(k)}$ for all $T \in L(V,V)$.
