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10 Nov 2019
Let T : V rightarrow W be a linear transformation from the vector space V to the vector space W. Let S be a set of vectors in V and let S' = T(S) be the set of the images of these vectors under this linear transformation. Show that if S' is linearly independent then S was already linearly independent. Is the converse true, i.e. if S is linearly independent, does this mean that S' is automatically linearly independent?
Let T : V rightarrow W be a linear transformation from the vector space V to the vector space W. Let S be a set of vectors in V and let S' = T(S) be the set of the images of these vectors under this linear transformation. Show that if S' is linearly independent then S was already linearly independent. Is the converse true, i.e. if S is linearly independent, does this mean that S' is automatically linearly independent?
Nestor RutherfordLv2
28 May 2019