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Homework Help: Beginner's linear algebra question

  1. Apr 5, 2006 #1
    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. jcsd
  3. Apr 5, 2006 #2

    0rthodontist

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    Science Advisor

    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?
     
  4. Apr 5, 2006 #3
    Well, i feel stupid. It was staring me right in the face. Thanks a lot!
     
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