7. Systems of Equations & Matrices

Solve for X in the matrix equation 3X+A = B where

Write the augmented matrix for each system and give its dimension. Do not solve.

2x + y + z - 3 = 0

3x - 4y + 2z + 7 = 0

x + y + z - 2 = 0

In Exercises 16–24, write the partial fraction decomposition of each rational expression.3x/(x - 2)(x^2 + 1)

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

Perform the indicated matrix operations given that A, B and C are defined as follows. If an operation is not defined, state the reason.

4B - 3C

Write the partial fraction decomposition of each rational expression. x/(x² +2x -3)

Exercises 57–59 will help you prepare for the material covered in the next section. Subtract: $\(\frac{3}{x - 4}\) - \(\frac{2}{x + 2}\)$

Solve each system, using the method indicated.

3x + y = -7

x - y = -5 (Gaussian elimination)

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

In Exercises 9 - 16, find the following matrices: b. A - B

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 9 - 16, find the following matrices: b. A - B

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

In Exercises 9 - 16, find the following matrices: a. A + B

Solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

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