(Step-by-Step) Find the LU decomposition of A algebraically, then use it to solve the system A x=b. Clearly identify your answers for L, U, x, and y.
Question: Find the LU decomposition of \(A\) algebraically, then use it to solve the system \(A x=b\). Clearly identify your answers for \(L\), \(U\), \(x\), and \(y\).
\[A=\left[\begin{array}{cccc} 1 & -2 & -2 & -3 \\ 3 & -9 & 0 & -9 \\ -1 & 2 & 4 & 7 \\ -3 & -6 & 26 & 2 \end{array}\right], b=\left[\begin{array}{l} 1 \\ 6 \\ 0 \\ 3 \end{array}\right]\]
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