[Solution] a) Find an LU-factorization of the coefficient matrix of the given linear system A x=b, where
Question: a) Find an LU-factorization of the coefficient matrix of the given linear system \(A x=b\), where
\[A=\left[\begin{array}{ccc} 2 & 4 & -4 \\ 1 & -4 & 3 \\ -6 & -9 & 10 \end{array}\right] \text { and } b=\left[\begin{array}{c} 12 \\ -21 \\ -24 \end{array}\right]\]That is, decompose the matrix \(A\) into an lower triangular matrix \(L\), and an upper triangular matrix \(U\)
b) Using the matrices \(L\) and \(U\) obtained in part (a), solve the non-homogeneous system by using a forward substitution followed by a backward substitution.
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