Diagonal matrix/Linear system/Solution method/Exercise

Let

${}D={\begin{pmatrix}d_{11}&0&\cdots &\cdots &0\\0&d_{22}&0&\cdots &0\\\vdots &\ddots &\ddots &\ddots &\vdots \\0&\cdots &0&d_{n-1\,n-1}&0\\0&\cdots &\cdots &0&d_{nn}\end{pmatrix}}\,$

be a diagonal matrix, and ${}c={\begin{pmatrix}c_{1}\\\vdots \\c_{n}\end{pmatrix}}$ an ${}n$-tuple over a field ${}K$, and let ${}x={\begin{pmatrix}x_{1}\\\vdots \\x_{n}\end{pmatrix}}$ be a tuple of variables. What is specific about the system of linear equations

${}Dx=c\,,$

and how can you solve it?

Create a solution