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Math Help - MATRICES (cramer's rule) help needed

  1. #1
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    MATRICES (cramer's rule) help needed

    MATRICES
    Solve the following . ( Cramer's Rule )

    Q) x+2y+3z=7
    3x+4y+2z=9
    2x+5y+4z=9
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  2. #2
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    Quote Originally Posted by raza9990 View Post
    MATRICES
    Solve the following . ( Cramer's Rule )

    Q) x+2y+3z=7
    3x+4y+2z=9
    2x+5y+4z=9
    What help do you want? You cite Cramer's rule. Do you know what that is?

    Cramer's rule says that the solutions of a system of equations
    a_{11}x+ a_{12}y+ a_{13}z= b_1
    a_{21}x+ a_{22}y+ a_{23}z= b_2
    a_{31}x+ a_{32}y+ a_{33}z= b_3

    are given by
    x=\frac{\left|\begin{array}{ccc}b_1 & a_{12} & a_{13} \\ b_2 & a_{22} & a_{23} \\ b_3 & a_{32} & a_{33}\end{array}\right|}{\left|\begin{array}{ccc}  a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|}

    y=\frac{\left|\begin{array}{ccc}a_{11} & b_2 & a_{13}\\ a_{21} &  b_2 & a_{23}\\ a_{31} & b_3 & a_{33}\end{array}\right|}{\left|\begin{array}{ccc}  a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|}

    z=\frac{\left|\begin{array}{ccc}a_{11} & a_{12} & b_1 \\ a_{21} & a_{22} & b_2 \\ a_{31} & a_{32} & b_3\end{array}\right|}{\left|\begin{array}{ccc}a_{  11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|}

    Put in the numbers for your equations and calculate the determinants. Have you done that yet?
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    What help do you want? You cite Cramer's rule. Do you know what that is?

    Cramer's rule says that the solutions of a system of equations
    a_{11}x+ a_{12}y+ a_{13}z= b_1
    a_{21}x+ a_{22}y+ a_{23}z= b_2
    a_{31}x+ a_{32}y+ a_{33}z= b_3

    are given by
    x=\frac{\left|\begin{array}{ccc}b_1 & a_{12} & a_{13} \\ b_2 & a_{22} & a_{23} \\ b_3 & a_{32} & a_{33}\end{array}\right|}{\left|\begin{array}{ccc}  a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|}

    y=\frac{\left|\begin{array}{ccc}a_{11} & b_2 & a_{13}\\ a_{21} &  b_2 & a_{23}\\ a_{31} & b_3 & a_{33}\end{array}\right|}{\left|\begin{array}{ccc}  a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|}

    z=\frac{\left|\begin{array}{ccc}a_{11} & a_{12} & b_1 \\ a_{21} & a_{22} & b_2 \\ a_{31} & a_{32} & b_3\end{array}\right|}{\left|\begin{array}{ccc}a_{  11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|}

    Put in the numbers for your equations and calculate the determinants. Have you done that yet?
    plz can u solve it for me.
    i cant figure it out
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  4. #4
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    Talking

    You've been given the complete set-up for applying Cramer's Rule. All that remains is the plug-in-chug, computing the numerical values of the determinants (perhaps in your calculator or other technology), and simplifying the resulting fractions.

    Where are you stuck? Please be complete. Thank you!
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