C^2/(2-7i,-3+2i) and (5+6i,3-17i)/Linearly independent/Exercise

Establish if in ${}\mathbb {C} ^{2}$ the two vectors

${\begin{pmatrix}2-7{\mathrm {i} }\\-3+2{\mathrm {i} }\end{pmatrix}}{\text{ and }}{\begin{pmatrix}5+6{\mathrm {i} }\\3-17{\mathrm {i} }\end{pmatrix}}$

form a basis.

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