Suppose there is a matrix equation such that:
$Ax = b$
where $A$ is given, which is an upper triangular matrix, and $b$ is given.
Then, $x$ and $b$ are perturbed by vectors $p$ and $q$ such that:
$A(x+p) = (b+q)$
The question asks to solve for $p$ in terms of $q$.
To approach this, I am thinking of finding $x$ by using the first equation, and then plug that $x$ into the second equation. Then, I can solve $p$ in terms of $q$. Do you think this (plugging in $x$ to the second equation) is acceptable? That is, is $x$ the same in both equations?