LU decomposition

Consider a system of linear equations $PX = Q$ where $P \in \mathbb{R}^{3 \times 3}$ and $Q \in \mathbb{R}^{3 \times 1}$. Suppose $P$ has an LU decomposition, $P = LU$, where $L =...

Consider a system of linear equations $P X=Q$ where $P \in \mathbb{R}^{3 \times 3}$ and $Q \in \mathbb{R}^{3 \times 3}$. Suppose $P$ has an $L U$ decomposition, $P=L U$, where $$L=...

Consider solving the following system of simultaneous equations using LU decomposition. x 1 + x 2 $$-$$ 2x 3 = 4 x 1 + 3x 2 $$-$$ x 3 = 7 2x 1 + x 2 $$-$$ 5x 3 = 7 where L and U ar...

In the LU decomposition of the matrix $$\left[ {\matrix{ 2 & 2 \cr 4 & 9 \cr } } \right]$$, if the diagonal elements of U are both 1, then the lower diagonal entry $${l_{22}}$$ of...