Problem 3. Suppose L: V W is a linear transformation from a vector space V into a vector space W. The preimage of a subspace of W is the set of all vectors in V whose images are in the subspace. That...

Problem 3. Suppose L: V W is a linear transformation from a vector space V into a vector space W. The preimage of<br>a subspace of W is the set of all vectors in V whose images are in the subspace. That is, if U C W is a subspace<br>of W, then the preimage is defined as<br>L-(U) := {v E V such that L(7) EU}.<br>Prove that L-U) is a vector subspace of V.<br>

Extracted text: Problem 3. Suppose L: V W is a linear transformation from a vector space V into a vector space W. The preimage of a subspace of W is the set of all vectors in V whose images are in the subspace. That is, if U C W is a subspace of W, then the preimage is defined as L-(U) := {v E V such that L(7) EU}. Prove that L-U) is a vector subspace of V.

Jun 05, 2022

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Problem 3. Suppose L: V W is a linear transformation from a vector space V into a vector space W. The preimage of a subspace of W is the set of all vectors in V whose images are in the subspace. That...

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