This is the matrix which I'm trying to LU decompose by Gaussian elimination. $$A=\begin{pmatrix} 2&1 &-4 \\ 2&1 &-2 \\ 6&3 &-11 \end{pmatrix}$$ I get to this by performing the row operations: $$\begin{pmatrix} 2&1 &-4 \\ 2&1 &-2 \\ 6&3 &-11 \end{pmatrix} \sim \begin{pmatrix} 2 &1 &-4 \\ 0&0 &2 \\ 0&0 &1 \end{pmatrix} = U $$
$$\therefore L = \begin{pmatrix} 1 &0 &0 \\ 1&1 &0 \\ 3&0 &1 \end{pmatrix}$$
This is however obviously incorrect since $$LU\neq A$$ I sslo attempted this problem using partial pivoting but run into the same problem. Can someone guide me where I'm making a mistake and how do I proceed to finding the LU decomposition? p.s. I'm relatively new to Linear Algebra and LU decomposition.
You miscopied $-4$ as $4$ in $U$. Once you fix this, $LU=A$.