7. Systems of Equations & Matrices

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

A - C

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

Write the equations in standard form, then represent the system using an augmented matrix.

$3x+5y-9=0$

$8x=-4y+3$

Find the quadratic function y = ax²+bx+c whose graph passes through the given points. (−1, 6), (1, 4), (2, 9)

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

Write the partial fraction decomposition of each rational expression. 4x²+13x-9/x (x − 1)(x+3)

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

Find the partial fraction decomposition for each rational expression. 5-2x / (x² + 2)(x - 1)

Solve each system, using the method indicated.

5x + 2y = -10

3x - 5y = -6 (Gauss-Jordan)

Answer each question. By what expression should we multiply each side of 5/((3x(2x + 1)) = A/(3x) + B/(2x + 1) so that there are no fractions in the equation?

Answer each question. By what expression should we multiply each side of (3x - 2)/(x + 4)(3x^2 + 1) = A/(x + 4) + (Bx + C)/(3x^2 + 1) so that there are no fractions in the equation?

Find the quadratic function y = ax^2 + bx + c whose graph passes through the points (1, 4), (3, 20), and (-2, 25).

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

$\(\begin{cases}\)3a - b - 4c = 3 \\2a - b + 2c = -8 \\(\a\) + 2b - 3c = 9\(\end{cases}\)$

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

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