(4.1) Let V, V, and Vs be vector spaces over a field F. Let T: VV and SV₂V₁ be linear transformations. (a) Show that ST: VV is a linear transformation. (b) Show that ker TC ker (ST) and im (ST) C im S. (c) Deduce that ST can only be bijective if T is injective and S is surjective. (3) (4) (3)

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