Using the General Interpolation Framework

This example shows how to determine whether a given interpolation function can interpolate the given data

Problem:

Given where and . Does there exist a function that interpolates the data ?

Solution:

We have so our corresponding system looks like:
Subbing in our values for we get the following system:
From this we can easily see that since the there will be no solutions.

Problem:

What if ?

Solution:

We have so our corresponding system looks like:
Subbing in our values for we get the following system:
From this we can use Gaussian Elimination to put into it's Row-Echelon-Form (REF) to determine whether there is a soultion:
So now we can tell that since the there will be a unique solution.