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(Solved): Suppose V and W are vector spaces, and T : V W is a linear transformation. Let {v1, . . . , vp} ...



Suppose V and W are vector spaces, and T : V → W is a linear transformation. Let {v1, . . . , vp} be a subset of V . Show that if {v1, . . . , vp} is linearly dependent in V , then the set of images, {T(v1), . . . , T(vp)}, is linearly dependent in W.



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