Perform one step of row reduction, in order to calculate the values for $x$ and $y$ by back substitution. Then calculate the values for $x$ and for $y$. Also calculate the determinant of the original matrix.

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(Note: since the determinant is unchanged by row reduction it will be easier to calculate the determinant of the row reduced matrix.) $$\left[\begin{array}{cc} -3+i &-3+3i\cr 5 &-3+2i \end{array}\right] \left\lbrack \begin{array}{c} x \\ y \end{array} \right\rbrack = \left[\begin{array}{c} -1-13i\cr -6-3i \end{array}\right]$$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $-3+i$ $-3+3i$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ $0$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $x$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ $y$

$=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $-1-13i$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

$x =$
$y =$
$\mbox{det} =$