7. Systems of Equations & Matrices

Write the system of equations associated with each augmented matrix . Do not solve.

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 1/x(x-1)

Solve each system in Exercises 25–26. $\(\begin{cases}\[\frac{x + 2}{6}\) - \(\frac{y + 4}{3}\) + \(\frac{z}{2}\) = 0 \\\(\frac{x + 1}{2}\) + \(\frac{y - 1}{2}\) - \(\frac{z}{4}\) = \(\frac{9}{2}\) \\\(\frac{x - 5}{4}\) + \(\frac{y + 1}{3}\) + \(\frac{z - 2}{2}\) = \(\frac{19}{4}\]\end{cases}\)$

Write the augmented matrix for each system of linear equations.

$\(\begin{cases}\)x - y + z = 8 \\(\y\) - 12z = -15 \\(\z\) = 1\(\end{cases}\)$

Find the following matrices: $A+B$

$A = \(\begin{bmatrix}\)2 \\-4 \\1\(\end{bmatrix}\), B = \(\begin{bmatrix}\)-5 \\3 \\-1\(\end{bmatrix}\)$

Write the augmented matrix for each system of linear equations.

$\(\begin{cases}\)5x - 2y - 3z = 0 \\(\x\) + y = 5 \\2x - 3z = 4\(\end{cases}\)$

In Exercises 9 - 16, find the following matrices: c. - 4A

Solve each system in Exercises 5–18. $\(\begin{cases}\)3x + 2y - 3z = -2 \\2x - 5y + 2z = -2 \\4x - 3y + 4z = 10\(\end{cases}\)$

Perform the indicated Row Operation.

ADD $R_1+2\(\cdot\) R_3\(\rightarrow\) R_1$

Find the partial fraction decomposition of 4x²+5x-9/(x³- 6x-9)

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\(\end{cases}\)$

Use the Gauss-Jordan method to solve each system of equations. For systems in two variables with infinitely many solutions, write the solution with y arbitrary. For systems in three variables with infinitely many solutions, write the solution set with z arbitrary.

x + y = 5

x - y = -1

Write the system of equations represented by the augmented matrix shown.

In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. -5(A+D)

Solve each system in Exercises 5–18. $\(\begin{cases}\)3(2x + y) + 5z = -1 \\2(x - 3y + 4z) = -9 \\4(1 + x) = -3(z - 3y)\(\end{cases}\)$