C^2/(2+7i,3-i) and (15+26i,13-7i)/Linearly independent/Exercise

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

${\begin{pmatrix}2+7{\mathrm {i} }\\3-{\mathrm {i} }\end{pmatrix}}{\text{ and }}{\begin{pmatrix}15+26{\mathrm {i} }\\13-7{\mathrm {i} }\end{pmatrix}}$

form a basis.

Create a solution