Point Xj is linear combination of rest of the other points ?

[blunderboy]

I remember in lecture 7, professor used a property

For any d+2 points, we can write

Xj as linear combination of rest of the points.

Q1. What is the proof for this property ?

Let us take an example: d = 1 and points are (5,10,7)
Q2. How do we write 7 in terms of 5 and 10 ?

[yaser]

Originally Posted by blunderboy

I remember in lecture 7, professor used a property

For any d+2 points, we can write

Xj as linear combination of rest of the points.

Q1. What is the proof for this property ?

Let us take an example: d = 1 and points are (5,10,7)
Q2. How do we write 7 in terms of 5 and 10 ?

Take a look at http://en.wikipedia.org/wiki/Linear_independence

For , the vectors are two-dimensional () because of the zeroth coordinate, but to answer your specific question, has many solutions, for instance, and .

[blunderboy]

Thank you professor..I was under impression we have to take only integer values for Ai. I will go through the linear independence once from wiki. Thanks for the link. I think that will make things clear to me.

Thanks a lot!!

[yaser]

You are most welcome.