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Vectors & Spaceseasy
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If the standard matrix of a transformation T:R2→R2T: \mathbb{R}^2 \to \mathbb{R}^2T:R2→R2 maps e1↦⟨3,1⟩\mathbf{e}_1 \mapsto \langle 3, 1 \ranglee1​↦⟨3,1⟩ and e2↦⟨−1,2⟩\mathbf{e}_2 \mapsto \langle -1, 2 \ranglee2​↦⟨−1,2⟩, what vector does T(⟨2,3⟩)T(\langle 2, 3 \rangle)T(⟨2,3⟩) produce?