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

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Dec 26, 2024
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- 11.8: Solving Systems with Cramer's Rule
- 12: Analytic Geometry

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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.

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

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

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