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(a) Find the inverse of the matrix

$A = \left[ \begin{array}{rrr} 3 & 6 & -13\\ 1 & 3 & -6\\ 1 & 2 & -4 \end{array} \right]$

$A^{-1}=$

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

(b) Use the answer from part (a) to solve the linear system

$\left\{ \begin{array}{rcrcrcr} 3 x_1 & + & 6 x_2 & - & 13 x_3 & = & -1 \cr x_1 & + & 3 x_2 & - & 6 x_3 & = & 1 \cr x_1 & + & 2 x_2 & - & 4 x_3 & = & -1 \end{array} \right.$

$\left[ \begin{array}{r} x_1 \\ x_2 \\ x_3 \end{array} \right]$

$\quad =$

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

You can earn partial credit on this problem.