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Math Help - Cramer's Rule

  1. #1
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    Cramer's Rule

    Solve the following system; if the system is inconsistent say so. Use Cramer's Rule to obtain solution.

    -9x + -4y + -6z = 85

    -16x + -6y + 37z = 81

    -7x + 8y + -4z = 75.

    I am able to work this when there is just two sets of equations but I am having trouble figuring out three of them.
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  2. #2
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    \begin{aligned} \bold{Ax} & = \bold{B} \\ \left[\begin{array}{ccc} -9 & -4 & -6 \\ -16 & -6 & 37  \\ -7 & 8 & -4 \end{array}\right]  \begin{bmatrix} x \\ y \\ z \end{bmatrix} & = {\color{red}\begin{bmatrix} 85 \\ 81 \\ 75 \end{bmatrix} }\end{aligned}

    Cramer's Rule says that:

    x = \frac{\left| \begin{array}{ccc} {\color{red}85} & -4 & -6 \\ {\color{red}81} & -6 & 37 \\ {\color{red}75} & 8 & -4 \end{array} \right|}{\det (A)}..... y = \frac{\left|\begin{array}{ccc} -9 & {\color{red}85} & -6 \\ -16 & {\color{red}81} & 37  \\ -7 & {\color{red}75} & -4 \end{array}\right|}{\det (A)}..... z = \frac{\left| \begin{array}{ccc} -9 & -4 & {\color{red}85} \\ -16 & -6 & {\color{red}81} \\ -7 & 8 & {\color{red}75} \end{array}\right|}{\det (A)}
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