Past exam of the mathematics course of the University of Cambridge / 2020 / ib / Paper 1 / 5C (Numerical Analysis)

Gaussian elimination gives the LU decompositionThe prescribed diagonal entries of $L$ are visible, and direct multiplication gives $LU=A$.

First solve $L\mathbf{y}=\mathbf{b}$ by forward substitution:Then solve $U\mathbf{x}=\mathbf{y}$ by backward substitution, obtainingDirect substitution verifies $A\mathbf{x}=\mathbf{b}$.