Determine if the statement is true or false and justify your

Determine if the statement is true or false, and justify your answer. The range of a linear transformation must be a subset of the domain.

Solution

If L is a linear transformation from a vector space V to a vector space W, then the range of L is the set of all vectors w in W such that there is a v in V with L(v) = w. The range of a linear transformation L from V to W is a subspace of W which is the co-domain of L and NOT the domain. Therefore, the given statement is false.