1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Cramer's Rule Original Problem

  1. Mar 20, 2009 #1
    1. The problem statement, all variables and given/known data

    Let the curve

    A + By + Cx + Dy^2 + Exy + x^2 = 0

    be given. It passes through the points (x_1, y_1),...,(x_5, y_5). Determine the A, B, C, D, and E.

    2. Relevant equations

    3. The attempt at a solution

    To create the system, I plug in each x_n and y_n into the given curve equation...

    [1, y_1, x_1, (y_1)^2, (x_1)(y_1), (x_1)^2]
    [1, y_2, x_2, (y_2)^2, (x_2)(y_2), (x_2)^2]
    [1, y_3, x_3, (y_3)^2, (x_3)(y_3), (x_3)^2]
    [1, y_4, x_4, (y_4)^2, (x_4)(y_4), (x_4)^2]
    [1, y_5, x_5, (y_5)^2, (x_5)(y_5), (x_5)^2]

    But, what do I do from here? Replace a row with vector b (all 0's in this case) and solve x = determinant of new matrix/determinant of original matrix. Then repeat for each row? Does the fact that there are x^2 and y^2 in the matrix matter at all or not?
  2. jcsd
  3. Mar 20, 2009 #2


    Staff: Mentor

    It doesn't matter that the variables x, y, x^2, y^2, and xy aren't linear. You're solving for the constants A, B, C, D, and E, and your equations are linear in these constants.

    When you substitute the known x and y values into the equation, your first equation will be:
    A + y_1*B + x_1*C + (y_1)^2 * D + (x_1)(y_1)*E = -(x_1)^2

    All five equations will look like this but will involve the other four pairs of x and y values.

    Your matrix will be a 5 row by 6 column augmented matrix that you can solve either by row reduction or by the use of Cramer's rule.
  4. Mar 20, 2009 #3
    Thank you!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook