ref attachment
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.
And the final answer should be:
47) Consider the matrix..
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.
Any cubic polynomial can be written in the form and then .
Saying that it has a horizontal tangent at (1, -2) tells you two things: its value at x= 1 is and its derivative there is . Do the same at x= -1 to get four equations for a, b, c, and d.
[quote]29) Use a system of equations to write the partial fraction decomposition of the rational expression. Then solve the system using matrices.
Multiply both sides of the equation by to get
Equating coefficients, A+ B= 4, 2A+ C= 0, and A- B+ C= 0.
Those correspond to the matrix equation
Row reduce the matrix just as you would to solve it. Since there are only two rows, that is simple: Add 3 times the first row to the second to getAnd the final answer should be:
47) Consider the matrix..
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.
That last row corresponds to (4+3k)y= 7. To solve that you must divide by 4+ 3k which you cannot do if 4+ 3k= 0.
True, of course. You can find the reduced row-echelon form by following a specific formula which, if done correctly, will always give the same result for the same matrix.58) True or false: Every matrix has a unique reduced row-echelon form.
Thank you in advance. I appreciate it.