Matrix/C/2+5i 1-2i 3-4i 6-2i/Invertible/Solution for 54+72i 0/Exercise

a) Determine if the complex matrix

${}M={\begin{pmatrix}2+5{\mathrm {i} }&1-2{\mathrm {i} }\\3-4{\mathrm {i} }&6-2{\mathrm {i} }\end{pmatrix}}\,$

is invertible.

b) Find a solution to the inhomogeneous linear system of equations

${}M{\begin{pmatrix}z_{1}\\z_{2}\end{pmatrix}}={\begin{pmatrix}54+72{\mathrm {i} }\\0\end{pmatrix}}\,.$

To solution