Question: does x^2 mean (as it usually does) Or does it mean (as I suspect it does)
Algebra: find all the solutions of each system of equations?
X^1 - 2X^2 + X^3 = 1
X^2 - 2X^3 + X^4 = 0
X^3 - 2X^4 + X^5 = 2
X^4 - 2X^5 + X^6 = 0
X^5 - 2X^6 + X^7 = 1
im not sure how to start such a big system of equations ....do you have to isolate all the different x's(x^1,x^2....)?
any help much appreciated!!!!
Interesting. Your system looks like a discretization of a DE. Anyway. Here's your system in matrix form:
Correct? I would start doing ERO's on the augmented matrix
What do you get?
[EDIT] Actually, you can do the back substitution immediately, because your matrix is upper triangular. I think you'll need two parameters to describe all of the solutions.
Well, you don't have enough equations to get a unique solution. You're going to have a two-parameter family of solutions (I get two from the fact that you have 7 unknowns and 5 equations. 7 - 5 = 2.) What I would do is use two parameters and Then you take the last equation there and solve for as follows:
so
Now that you have you can proceed to obtain , and so on. Make sense? Your final answer should look like this:
where through are known, and through are known. You've already got the following:
Your answer is equivalent in form to the form that I gave. Which one is preferable depends on your teacher. If I were teaching, I'd accept either. To convert from one to the other, just read off the coefficients. For example:
which is the constant vector. Make sense?