Homework Help: Beginner's linear algebra question

1. Apr 5, 2006

lezardo

Hi everyone! I recently started taking a basic linear algebra course at my university and I'm already having problems. I used to be pretty good at math in general, but I guess I've unlearned everything over the years. Any help would be appreciated, thanks!

A.
Two points on a plane with the coordinates (x0,y0) and (x1,y1) define a graph with the form:
y = c1x + c0 (polynomial of the 1. degree).

1)Formulate a system of linear equations to find the coefficients of this function.
2) Solve this system of equations to find the function which runs through the points (1;3) and (2;4).

B.
n + 1 points on a plane [(x0, y0), (x1, y1),…; (xn, yn)] define a polynomial of the nth degree:
y = cnx^n + …+ c2x^2 + c1x + c0.

1)Formulate a system of linear equations to find the coefficients of this polynomial.
2) Solve this system to find the polynomial which runs through the points (0;1), (1;10), (2,33) and (3,64).

P.S. Hints or something like that would also be great. It's really frustrating sitting here with nothing but "duhhhhh" in my head.

2. Apr 5, 2006

0rthodontist

Do you understand the question? It's asking you to find the equation of the polynomial whose graph passes through those points. Here is a hint on part A. The equation you are trying to find is y = c1x + c0 (you are trying to find the c's). You know that the point (x0, y0) satisfies this equation and so does (x1, y1). So you can write, for example
y0 = c1x0 + c0
where y0 and x0 are KNOWN and c1 and c0 are UNKNOWN.
Can you figure it out now?

3. Apr 5, 2006

lezardo

Well, i feel stupid. It was staring me right in the face. Thanks a lot!