7. Systems of Equations & Matrices

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (x²)/(x⁴ - 1)

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x² - 3x - 4)/(x³ + x² - 2x)

Find the partial fraction decomposition for each rational expression. 5-2x / (x² + 2)(x - 1)

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}w + 2x + 3y - z = 7 \\2x - 3y + z = 4 \\w - 4x + y = 3\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}w + x - y + z = -2 \\2w - x + 2y - z = 7 \\-w + 2x + y + 2z = -1\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}x + y - 2z = 2 \\3x - y - 6z = -7\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}x + 2y + 3z = 5 \\y - 5z = 0\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}2x + y - z = 2 \\3x + 3y - 2z = 3\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}w - 3x + y - 4z = 4 \\-2w + x + 2y = -2 \\3w - 2x + y - 6z = 2 \\-w + 3x + 2y - z = -6\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}2w + x - y = 3 \\w - 3x + 2y = -4 \\3w + x - 3y + z = 1 \\w + 2x - 4y - z = -2\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}w - 2x - y - 3z = -9 \\w + x - y = 0 \\3w + 4x + z = 6 \\2x - 2y + z = 3\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}8x + 5y + 11z = 30 \\-x - 4y + 2z = 3 \\2x - y + 5z = 12\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}3x + 4y + 2z = 3 \\4x - 2y - 8z = -4 \\x + y - z = 3\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}5x + 12y + z = 10 \\2x + 5y + 2z = -1 \\x + 2y - 3z = 5\end{cases}$

In Exercises 8–11, use Gaussian elimination to find the complete solution to each system, or show that none exists.