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Find the $LU$ factorization of $A= \left[\begin{array}{cccc} 2 &-1 &1 &-1\cr -6 &5 &0 &4\cr 2 &-7 &-11 &-7\cr 6 &7 &27 &15 \end{array}\right]$ and use it to solve the system $\left[\begin{array}{cccc} 2 &-1 &1 &-1\cr -6 &5 &0 &4\cr 2 &-7 &-11 &-7\cr 6 &7 &27 &15 \end{array}\right] \left[\begin{array}{c} x_{1}\cr x_{2}\cr x_{3}\cr x_{4}\cr \end{array}\right] = \left[\begin{array}{c} 1\cr 4\cr -23\cr 55 \end{array}\right].$

$A = LU =$ $\left[\Rule{0pt}{4.8em}{0pt}\right.$ $\left]\Rule{0pt}{4.8em}{0pt}\right.$ $\left[\Rule{0pt}{4.8em}{0pt}\right.$ $\left]\Rule{0pt}{4.8em}{0pt}\right.$

$\vec{x} =$ $\left[\Rule{0pt}{4.8em}{0pt}\right.$ $\left]\Rule{0pt}{4.8em}{0pt}\right.$

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