Can matrix algebra solve equations with squared variables?

[bobsmith76]

Homework Statement

For the last 90 minutes I've been working on this problem.

https://www.physicsforums.com/showthread.php?t=582722

I don't know if it's been solved but I don't care because I really like the challenge of it. I'm at the point now in the problem where my knowledge of matrix algebra is coming up short. I need to know

1. where to look to find out how to solve a 6 by 2 matrix.
2. whether it is even possible to use matrix algebra if some of the variables are taken to the second power
3. whether the exact values of the below variables can even be found or am i just wasting my time on a dead end.

here are the equations I have worked out

s² - 6s + h² - 8h - p² + 10p = 0, p < 5
s² + h² - p² = 0

Again, I'm not sure if variables of different powers can be used in a matrix, they probably cannot, but if they can that would make for the following matrix

1 -6 1 -8 -1 10
1 0 1 0 -1 0

I also have another equation

s² + 6s + h² + 2sd + 6d - 9 = 0

but that would expand my matrix into 3 by 9 which might be larger than necessary.

I'm going to try to express h and s in terms of p right now, but it will be very clumsy and will take a while.

 

[genericusrnme]

Your system is underdetermined, you've got 3 equations and 4 unknowns.