11.8E: Solving Systems with Cramer's Rule (Exercises)
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.
\(\frac{3}{10} x-\frac{1}{5} y-\frac{3}{10} z=-\frac{1}{50}\)
\(\frac{1}{10} x-\frac{1}{10} y-\frac{1}{2} z=-\frac{9}{50}\)
\(\frac{2}{5} x-\frac{1}{2} y-\frac{3}{5} z=-\frac{1}{5}\)