Mathematics II207810 marksNumerical: LU factorizationMatrix factorization
Find the LU factorization of
Find the LU factorization of $$\begin{bmatrix} 2 & 4 & -1 & 5 & -2 \ -4 & -5 & 3 & -8 & 1 \ 2 & -5 & -4 & 1 & 8 \ -6 & 0 & 7 & -3 & 1 \end{bmatrix}$$ [10]
$$A = \begin{bmatrix} 2 & 4 & -1 & 5 & -2 \ -4 & -5 & 3 & -8 & 1 \ 2 & -5 & -4 & 1 & 8 \ -6 & 0 & 7 & -3 & 1 \end{bmatrix}$$ We seek $A = LU$ with $L$ unit lower triangular ($4\times4$) and $U$ upper (echelon) form ($4\times5$). The multipliers used in Gaussian elimination fill in $L$. --- Mul...