91Ó°ÊÓ

Decompose into partial fractions. Check your answers using a graphing calculator. $$\frac{5 x^{3}+6 x^{2}+5 x}{\left(x^{2}-1\right)(x+1)^{3}}$$

Use the following matrix: $$\mathbf{A}=\left[\begin{array}{rrr}7 & -4 & -6 \\\2 & 0 & -3 \\\1 & 2 & -5\end{array}\right]$$. Evaluate \(|\mathbf{A}|\) by expanding across the first row.

Solve the system of equations. $$\begin{aligned} w+x-y+z &=0 \\ -w+2 x+2 y+z &=5 \\ -w+3 x+y-z &=-4 \\ -2 w+x+y-3 z &=-7 \end{aligned}$$

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

Solve the system of equations using Gaussian elimination or Gauss-Jordan elimination. Use a graphing calculator to check your answer. $$\begin{aligned} &5 x-2 y=-3\\\ &2 x+5 y=-24 \end{aligned}$$

At the 2014 Paralympic Games in Sochi, Russia, the top three countries - the Russian Federation, Ukraine, and the United States-won a total of 123 medals. Ukraine won 7 more medals than the United States. The Russian Federation won 37 more medals than the total amount won by Ukraine and the United States. (Source: International Paralympic Committee) How many medals did each of the top three countries win?

Use a graphing calculator to find \(\mathbf{A}^{-1}\), if it exists. $$\mathbf{A}=\left[\begin{array}{rrr}1 & 2 & -1 \\ -2 & 0 & 1 \\ 1 & -1 & 0\end{array}\right]$$

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

Decompose into partial fractions. Check your answers using a graphing calculator. $$\frac{6 x^{3}+5 x^{2}+6 x-2}{2 x^{2}+x-1}$$

Use a graphing calculator to find \(\mathbf{A}^{-1}\), if it exists. $$\mathbf{A}=\left[\begin{array}{rrr}7 & -1 & -9 \\ 2 & 0 & -4 \\ -4 & 0 & 6\end{array}\right]$$