7. Systems of Equations & Matrices

Write the partial fraction decomposition of each rational expression. $\(\frac{x^3 + x^2 + 2}{(x^2 + 2)^2}\)$

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

Find the partial fraction decomposition for each rational expression. See Examples 1–4. 1/(x(2x + 1)(3x² + 4))

Find the quadratic function y = ax²+bx+c whose graph passes through the given points. (−1,−4), (1,−2), (2, 5)

Solve each problem. See Examples 5 and 9. The sum of the measures of the angles of any triangle is 180°. In a certain triangle, the largest angle measures 55° less than twice the medium angle, and the smallest angle measures 25° less than the medium angle. Find the measures of all three angles.

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

BC + CB

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

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

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

Find the cubic function f(x) = ax³ + bx² + cx + d for which ƒ( − 1) = 0, ƒ(1) = 2, ƒ(2) = 3, and ƒ(3) = 12.

Solve each system in Exercises 12–13. The is a piecewise function

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. (3x+16)/(x + 1) (x − 2)²

Find the quadratic function f(x) = ax² + bx + c for which ƒ( − 2) = −4, ƒ(1) = 2, and f(2) = 0.

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

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x² - 3x - 4)/(x³ + x² - 2x)