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Math Help - Linear Systems and Matrices / Translations of Conics

  1. #1
    thoffman
    Guest

    Linear Systems and Matrices / Translations of Conics

    Solve the system of linear equations and check any solution algebraically.

    #20)

    5x - 3y + 2z = 3
    2x + 4y - z = 7
    x - 11y + 4z = 3

    Okay so I put this in my T1-84 in matrix a with the proper coefficent values.
    I use rref([A]) and this is the solution set I get-

    1 0 5/26 0
    0 1 -9/26 0
    0 0 0 1

    Generally the solution is in the last line of solutions. Anyhow, I am very confused on how to solve this by hand to get a solution. Also, is this a special case? A solution and walkthrough would be appreciated.

    Write the form or the partial fraction decomposition of the rational rexpression. Do not solve for constants.

    #50)

    x^2 - 3x + 2
    ----------------
    4x^3 + 11x^2

    As long as the highest degree is on the bottom it is not an irrational partial fraction right? I would like the solution and walkthrough on this as well.

    Find the center, foci, and vertices of the ellipse, and sketch its graph.

    #38)

    9x^2 + 4y^2 - 36x + 8y + 31 = 0

    I seperate these by terms correct?

    (9x^2 - 36x ) + (4y^2 + 8y ) = -31

    Do I factor this next?

    9(x^2 - 4x) + 4(4^2 + 2y) = -31

    If this is the correct track, I am lost from here.

    I would like the solution and walkthrough on this as well.

    Thanks in advance!
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  2. #2
    MHF Contributor red_dog's Avatar
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    \displaystyle\left\{\begin{array}{lll}5x-3y+2z=3\\2x+4y-z=7\\x-11y+4z=3\end{array}\right.
    Let \displaystyle A=\begin{pmatrix}5 & -3 & 2\\2 & 4 & -1\\1 & -11 & 4\end{pmatrix} be the matrix of system.
    We have \det A=0.
    Let \displaystyle d=\left|\begin{array}{cc}5 & -3\\2 & 4\end{array}\right|=26, so the matrix has grade 2.
    Let \displaystyle d_c=\begin{vmatrix}5 & -3 & 3\\2 & 4 & 7\\1 & -11 & 3\end{vmatrix}=364\neq 0\Rightarrowthe system is incompatible.
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  3. #3
    MHF Contributor red_dog's Avatar
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    50)

    \displaystyle \frac{x^2-3x+2}{4x^3+11x^2}=\frac{x^2-3x+2}{x^2(4x+1)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C  }{4x+11}
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