Suppose T V W is linear. If W, is a subspace of W, we define the...

 

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Suppose T V W is linear. If W, is a subspace of W, we define the inverse image 7-¹(W₁) to be all vectors in V whose image under T lies in W₁: explicitly, 7 (W₁)= (veV: T(v) E W₁). Show that T-1 (W₁) is a subspace of V. (Note that T-1 is not necessarily a function.) Suppose T V W is linear. If W, is a subspace of W, we define the inverse image 7-¹(W₁) to be all vectors in V whose image under T lies in W₁: explicitly, 7 (W₁)= (veV: T(v) E W₁). Show that T-1 (W₁) is a subspace of V. (Note that T-1 is not necessarily a function.)

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To show that T1W is a subspace of V we need to show that it ... View the full answer