Let U, W c V be vector spaces with V = U W and suppose that T E L(V). Define LE L(U,V) by (u) = u, and define T E L(V, U) as follows: If v = u + w with u E U and w e W, then T(v) = u. (a) Explain why 7 is well defined and is in L(V, U). (b) Show that if inTi = Tu, then U is T invariant and rTi = T\1.

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