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Mathematics LibreTexts

11.8E: Solving Systems with Cramer's Rule (Exercises)

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    56130
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    For the following exercises, find the determinant.

    71. \(\left|\begin{array}{cc}100 & 0 \\ 0 & 0\end{array}\right|\)

    72. \(\left|\begin{array}{ll}0.2 & -0.6 \\ 0.7 & -1.1\end{array}\right|\)

    73. \(\left|\begin{array}{ccc}-1 & 4 & 3 \\ 0 & 2 & 3 \\ 0 & 0 & -3\end{array}\right|\)

    74. \(\left|\begin{array}{ccc}\sqrt{2} & 0 & 0 \\ 0 & \sqrt{2} & 0 \\ 0 & 0 & \sqrt{2}\end{array}\right|\)

    For the following exercises, use Cramer's Rule to solve the linear systems of equations.

    75.

    \(4 x-2 y=23\)
    \(-5 x-10 y=-35\)

    76 .

    \(0.2 x-0.1 y=0\)

    \(-0.3 x+0.3 y=2.5\)

    77 .

    \(-0.5 x+0.1 y=0.3\)
    \(-0.25 x+0.05 y=0.15\)

    78.

    \(x+6 y+3 z=4\)

    \(2 x+y+2 z=3\)
    \(3 x-2 y+z=0\)

    79.

    \(4 x-3 y+5 z=-\frac{5}{2}\)

    \(\quad 7 x-9 y-3 z=\frac{3}{2}\)
    \(x-5 y-5 z=\frac{5}{2}\)

    80.

    \(\frac{3}{10} x-\frac{1}{5} y-\frac{3}{10} z=-\frac{1}{50}\)

    \(\frac{1}{10} x-\frac{1}{10} y-\frac{1}{2} z=-\frac{9}{50}\)
    \(\frac{2}{5} x-\frac{1}{2} y-\frac{3}{5} z=-\frac{1}{5}\)


    11.8E: Solving Systems with Cramer's Rule (Exercises) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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