91Ó°ÊÓ

Use a graphing calculator to find \(\mathbf{A}^{-1}\), if it exists. $$\mathbf{A}=\left[\begin{array}{rrrr}1 & -14 & 7 & 38 \\ -1 & 2 & 1 & -2 \\\ 1 & 2 & -1 & -6 \\ 1 & -2 & 3 & 6\end{array}\right]$$

Solve using the substitution method. Use a graphing calculator to check your answer. $$\begin{aligned} &x-2 y=3\\\ &2 x=4 y+6 \end{aligned}$$

Decompose into partial fractions. Check your answers using a graphing calculator. $$\frac{-17 x+61}{6 x^{2}+39 x-21}$$

Use the following matrix: $$\mathbf{A}=\left[\begin{array}{rrrr}1 & 0 & 0 & -2 \\\4 & 1 & 0 & 0 \\\5 & 6 & 7 & 8 \\\\-2 & -3 & -1 & 0\end{array}\right]$$ Use a graphing calculator to evaluate \(|\mathbf{A}|\).

Use a graphing calculator to find \(\mathbf{A}^{-1}\), if it exists. $$\mathbf{A}=\left[\begin{array}{rrrr}10 & 20 & -30 & 15 \\ 3 & -7 & 14 & -8 \\\ -7 & -2 & -1 & 2 \\ 4 & 4 & -3 & 1\end{array}\right]$$

Natural Fibers Clothing charges \$4 for shipping orders of \(\$ 25\) or less, \(\$ 8\) for orders from \(\$ 25.01\) to \(\$ 75,\) and \(\$ 10\) for orders over \(\$ 75 .\) One week, shipping charges for 600 orders totaled \(\$ 4280 .\) Eighty more orders for \(\$ 25\) or less were shipped than orders for more than \(\$ 75 .\) Find the number of orders shipped at each rate.

Solve the system of equations using Gaussian elimination or Gauss-Jordan elimination. Use a graphing calculator to check your answer. $$\begin{aligned} &4 x-8 y=12\\\ &-x+2 y=-3 \end{aligned}$$

Decompose into partial fractions. Check your answers using a graphing calculator. $$\frac{-4 x^{2}-9 x+8}{\left(3 x^{2}+1\right)(x-2)}$$

Evaluate the determinant. $$\left|\begin{array}{rrr}3 & 1 & 2 \\\\-2 & 3 & 1 \\\3 & 4 & -6\end{array}\right|$$

Solve using the substitution method. Use a graphing calculator to check your answer. $$\begin{aligned} &x-5 y=4\\\ &y=7-2 x \end{aligned}$$