Help with Notation for changing one or more element in n tuple

Question

I have $x=(x_1,x_2,x_3)$, what notation would best represent $(x_1,x_2’,x_3)$ or $(x_1,x_2’,x_3’)$?. I am currently using $x’$ to represent $(x_1’,x_2’,x_3’)$

Answer 1

You could write each such vector as $xA+x^\prime B$, for matrices $A,\,B$ you can find as an exercise. The choice of these $A,\,B$ depends on which of the partially-primed tuples you seek.