Explain why there cannot be a linear transformation $T: \mathbb{R}^2\to \mathbb{R}^2$ for which $T(1,1)=(2,3)$ and $T(3,3)=(1,4)$.
I have no clue how to start this problem. Wouldn't $T(4,4)=4T(1,1)=4(2,3)=(8,12)$
2026-03-28 01:05:59.1774659959
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Note that $(6,9)=3(2,3)=3T(1,1)\not=T(3,3)=(1,4)$