Math Solutions

[Steps Shown] Use the following LU factorization to (a) compute the determinant and (b) solve [A]x=b with b^T= [lll-10 44

Question: Use the following LU factorization to (a) compute the determinant and (b) solve \([A]\{x\}=\{b\}\) with \(\{b\}^{T}=\) \(\left[\begin{array}{lll}-10 & 44 & -26\end{array}\right]\)

\[\begin{aligned} [A]=[L][U]=&\left[\begin{array}{ccc} 1 & & \\ 0.6667 & 1 \\ -0.3333 & -0.3636 & 1 \end{array}\right] \\ & \times\left[\begin{array}{ccc} 3 & -2 & 1 \\ & 7.3333 & -4.6667 \\ & & 3.6364 \end{array}\right] \end{aligned}\]

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