5. Let V, W be vector spaces and T : V â W be a one-to-one linear transformation. Let S be a linearly independent subset of V and let v be a vector in V that is not in Span(S). Show that T (S âª {v}) is linearly independent.

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5. Let V, W be vector spaces and T : V â W be a one-to-one linear transformation. Let S be a linearly independent subset of V and let v be a vector in V that is not in Span(S). Show that T (S âª {v}) is linearly independent.

5. Let V, W be vector spaces and T : V â W be a one-to-one linear transformation. Let S be a linearly independent subset of V and let v be a vector in V that is not in Span(S). Show that T (S âª {v}) is linearly independent.

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5. Let V, W be vector spaces and T : V â W be a one-to-one linear transformation. Let S be a linearly independent subset of V and let v be a vector in V that is not in Span(S). Show that T (S âª {v}) is linearly independent.

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5. Let V, W be vector spaces and T : V â W be a one-to-one linear transformation. Let S be a linearly independent subset of V and let v be a vector in V that is not in Span(S). Show that T (S âª {v}) is linearly independent.