K^3/215/137/412/Basis/Exercise

Prove that in ${}\mathbb {R} ^{3}$, the three vectors

${\begin{pmatrix}2\\1\\5\end{pmatrix}}\,,{\begin{pmatrix}1\\3\\7\end{pmatrix}}\,,{\begin{pmatrix}4\\1\\2\end{pmatrix}}$

are a basis.

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