7. Systems of Equations & Matrices

In Exercises 27 - 36, find (if possible) the following matrices: a. AB b. BA 1 3 3 - 2 A = B = 5 3 - 1 6

In Exercises 16–24, write the partial fraction decomposition of each rational expression. (4x^3 + 5x^2 + 7x - 1)/(x^2 + x + 1)^2

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

Find the dimension of each matrix. Identify any square, column, or row matrices.

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (-3)/(x²(x² + 5))

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 + 8y - 6z = 14 \\3x + 4y - 2z = 8 \\(\x\) + 2y - 2z = 3\(\end{cases}\)$

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

Find the dimension of each matrix. Identify any square, column, or row matrices.

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

In Exercises 16–24, write the partial fraction decomposition of each rational expression. (4x^2 - 3x - 4)/x(x + 2)(x - 1)

In Exercises 5 - 8, find values for the variables so that the matrices in each exercise are equal. $\(\begin{bmatrix}\)x \\4\(\end{bmatrix}\)=\(\begin{bmatrix}\)6 \\(\y\]\end{bmatrix}\)$

Write the augmented matrix for each system of linear equations.

$\(\begin{cases}\)2w + 5x - 3y + z = 2 \\3x + y = 4 \\(\w\) - x + 5y = 9 \\5w - 5x - 2y = 1\(\end{cases}\)$

Find the partial fraction decomposition for 1/x(x+1) and use the result to find the following sum:

Solve the system of equations by using row operations to write a matrix in REDUCED row-echelon form.

$4x+2y+3z=6$

$x+y+z=3$

$5x+y+2z=5$

What is the augmented matrix of the following system?

-3x + 5y = 2

6x + 2y = 7