# Linear Algebra Homework help

lovenkindness
Linear Algebra Homework help!!

## Homework Statement

Suppose a particular object is modelled as moving in an elliptical orbit centered at
the origin. Its nominal trajectory is described in rectangular coordinates (r;s) by the
constraint equation x1r^2 +x2s^2 +x3rs = 1, where x1; x2; and x3 are unknown parameters that specify the orbit. We have available the following noisy measurements of
the object’s coordinates (r;s) at ten different points on its orbit:

(0:6925;0:0592) (0:3582;0:4110) (0:2514;0:3763) (0:0764;0:5453)
(0:4249;0:3768) (0:6917;0:0252) (0:3831;0:2116) (0:0027;0:3801)
(0:0865;0:3628) (0:5428;0:2889)
Using the assumed constraint equation, arrange the given information in the form of
the linear system of equation Ax + b, where A is a known 10x3 matrix, b is a known
10 x1 vector, and x = (x1; x2; x3)^T.
This system of 10 equations in 3 unknowns is inconsistent. We wish to ﬁnd the solution x that minimizes the Euclidean norm of error Ax +b. Compare the solution obtained by using the following MATLAB invocations, each of which in principle gives the desired least-square-error solution:
(a). x = A\b
(b). x = pinv(A) *b
(c). x = inv(A'*A)*A'*b

Plot the ellipse that corresponds to your estimate of x. Attach the m-ﬁl

Homework Helper

Welcome to PF;
It helps to give it a shot and tell us about it.
You should have some examples of this sort of thing in your notes and your coursework to date so you do have someplace to start from. Show your reasoning until you get stuck and we'll be able to help where you get unstuck.

BTW: there are lots of ways to fit conics to noisy data ... when you work through from your notes, we'll be tipped off about which one you are supposed to be using.
So far it looks like a regularization problem.