I've done over 50 problems for a Linear Algebra class tonight and I'm sooo burnt out. I'm giving up on these ones.. if you can help me, that would be wonderful. Otherwise, I'm turning in what I have. Strangely enough, it's the odd problems that I already have solutions to that I don't understand. Got the even ones already.

11)In the "Polynomial Curve Fitting" section:

The graph of a cubic polynomial function has horizontal tangents at (1, -2) and (-1,2). Find an equation for the cubic and sketch its graph.

Somehow the answer is p(x) = -3x + x^3. Just want to know the steps.

29)Use a system of equations to write the partial fraction decomposition of the rational expression. Then solve the system using matrices.

$\displaystyle

\frac{4x^2}{(x+1)^2(x-1)} = \frac{A}{x-1}+\frac{B}{x+1}+\frac{C}{(x+1)^2}

$

And the final answer should be:

$\displaystyle

\frac{1}{1-x}+\frac{3}{1+x}-\frac{2}{(x+1)^2}

$

47)Consider the matrix..

$\displaystyle

A=\begin{bmatrix} 1 &k &2 \\ -3 &4 &1 \\ \end{bmatrix}

$

If A is the augmented matrix of a system of linear equations, find the value(s) of k such that the system is consistent.

(Answer is all real k not equal to -4/3. Just want to know how they got this so I understand it.

58)True or false: Every matrix has a unique reduced row-echelon form.

Thank you in advance. I appreciate it.