###### Definition3.4.3

Suppose a $$2\times2$$ matrix $$A$$ has columns $$\vvec_1$$ and $$\vvec_2\text{.}$$ If the pair of vectors is positively oriented, then the determinant of $$A\text{,}$$ denoted $$\det A\text{,}$$ is the area of the parallelogram formed by $$\vvec_1$$ and $$\vvec_2\text{.}$$ If the pair is negatively oriented, then $$\det A$$ is minus the area of the parallelogram.

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