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![Let \( L: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2} \) be a linear operator. If
\[
L\left((1,2)^{T}\right)=(-2,3)^{T}
\]
\[
L](https://media.cheggcdn.com/study/349/349914bb-1889-4a44-bd68-d23f16a8b547/image)
Expert Answer
We can use the fact that a linear operator is completely determined by its action on a basis of the vector space. Since the linear operator L maps fro