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Solving equations of upper triangular matrices

Suppose you have an equation like $R \cdot x = b$ with $R \in \mathbb{R}^{n \times n}$ and $x,b \in \mathbb{R}^n$. $b$ and $R$ are given and you want to solve for $x$. Example With $n=5$, the problem could look like this: $$\begin{pmatrix} 2 … Read More »

Solving equations of lower unitriangular matrices

Suppose you have an equation like $L \cdot x = b$ with $L \in \mathbb{R}^{n \times n}$ and $x,b \in \mathbb{R}^n$. $b$ and $L$ are given and you want to solve for $x$. Example With $n=5$, the problem could look like this: $$\begin{pmatrix} 1 … Read More »