Mathematics II20755 marksNumerical: LU factorizationMatrix factorization
Find LU factorization of the matrix beginbmatrix 2 & 5 6 & -7 endbmatrix
Find LU factorization of the matrix $\begin{bmatrix} 2 & 5 \ 6 & -7 \end{bmatrix}$ [5]
$$A = \begin{bmatrix} 2 & 5 \ 6 & -7 \end{bmatrix}$$ Goal: find $L$ (lower triangular, unit diagonal) and $U$ (upper triangular) such that $A = LU$. --- Pivot (1,1) = 2. Eliminate entry $a{21} = 6$. Multiplier: $$\ell{21} = \frac{6}{2} = 3$$ Row operation: $R2 \rightarrow R2 - 3R1$ $$\begin{bmat...