7. Systems of Equations & Matrices

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (2x^5 + 3x^4 - 3x^3 - 2x^2 + x)/(2x^2 + 5x + 2)

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

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (-x^4 - 8x^2 + 3x - 10)/((x + 2)(x^2 + 4)^2)

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

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

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

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists.w + 2x + 3y - z = 72x - 3y + z = 4w - 4x + y = 3

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists.w + x - y + z = - 22w - x + 2y - z = 7- w + 2x + y + 2z = - 1

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists.x + y - 2z = 23x - y - 6z = - 7

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists.x + 2y + 3z = 5y - 5z = 0

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists.2x + y - z = 23x + 3y - 2z = 3

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists.w - 3x + y - 4z = 4- 2w + x + 2y = - 23w - 2x + y - 6z = 2- w + 3x + 2y - z = - 6

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists.2w + x - y = 3w - 3x + 2y = - 43w + x - 3y + z = 1w + 2x - 4y - z = - 2

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists.w - 2x - y - 3z = - 9w + x - y = 03w + 4x + z = 62x - 2y + z = 3

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists.8x + 5y + 11z = 30- x - 4y + 2z = 32x - y + 5z = 12