7. Systems of Equations & Matrices

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

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (2x² -18x -12)/x³- 4x

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

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

Use the given row transformation to change each matrix as indicated.

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. (7x² -9x+3)/(x²+7)²

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

$\{\begin{array}{c}x+2y+3z=-5\\ 2x+y+z=1\\ x+y-z=8\end{array}$

Write the partial fraction decomposition of each rational expression. 6x²-x+1/(x³ + x² + x +1)

Write the partial fraction decomposition of each rational expression. 5x² -6x+7/(x − 1) (x² + 1)

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

In Exercises 19–20, a few steps in the process of simplifying the given matrix to row-echelon form, with 1s down the diagonal from upper left to lower right, and 0s below the 1s, are shown. Fill in the missing numbers in the steps that are shown.

Write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables.

$\(\begin{bmatrix}\)5 & 0 & 3 & \(\vert\) & -11 \\0 & 1 & -4 & \(\vert\) & 12 \\7 & 2 & 0 & \(\vert\) & 3\(\end{bmatrix}\)$

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

$\(\begin{cases}\)x + 3y = 0 \\(\x\) + y + z = 1 \\3x - y - z = 11\(\end{cases}\)$

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

Write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables.

$\(\begin{bmatrix}\)1 & 1 & 4 & 1 & \(\vert\) & 3 \\-1 & 1 & -1 & 0 & \(\vert\) & 7 \\2 & 0 & 0 & 5 & \(\vert\) & 11 \\0 & 0 & 12 & 4 & \(\vert\) & 5\(\end{bmatrix}\)$