I know that this is the solving system of linear equation problem.

But my question is why it is a problem the number of observation is lower than the number of predictors how can that thing happen?

Does not the data collection come from the delicate survey design or experimental design to the extent that they at least think about this thing?

If the data collection want to collect 45 variables to conduct research then why would he collect less than 45 observation? Did I miss something and although the model selection part also eliminated the non-improvement variables on the response and always the collected variable will be eliminated to 45-(45-p) right?

So then why would we face the non-unique solution in those case?

I know that this is the solving system of linear equation problem.

But my question is why it is a problem the number of observation is lower than the number of predictors how can that thing happen?

Does not the data collection come from the delicate survey design or experimental design to the extent that they at least think about this thing?

If the data collection want to collect 45 variables to conduct research then why would he collect less than 45 observation? Did I miss something and although the model selection part also eliminated the non-improvement variables on the response and always the collected variable will be eliminated to $45-(45-p)$ right?

So then why would we face the non-unique solution in those case?