Linear Algebra? (Or Differential Equation?)

1. Apr 3, 2012

mudkip123

Find un, vn, and tn in terms of n for the following system:
{
un+1 = -un + 2vn + tn
vn+1 = vn - tn
tn+1 = 2tn

For u0, v0, t0 given

This isn't homework, it's on a study guide for my midterm.

2. Apr 4, 2012

tiny-tim

welcome to pf!

hi mudkip123! welcome to pf!

you're looking for a combination an = Aun + Bvn + Ctn such that an+1 = Dan

3. Apr 4, 2012

Ray Vickson

First solve the third one $t_{n+1} = 2 t_n,$ to get $t_n = t_0 2^{n-1}.$ Now look at the second one $v_{n+1} = v_n -t_n.$ It gives $v_n = v_0 -\sum_{j=0}^{n-1} t_j,$ which is computable. Now you have $u_{n+1} = -u_n + f(n)$ with a known function f(n), so you can solve it easily: $$u_1 = f(0)-u_0, \; u_2 = f(1) - u_1 = f(1)-f(0) + u_0, \; u_3 = f(2) - u_2 = f(2)-f(1)+f(0) - u_0,$$ etc.

RGV

4. Apr 4, 2012

mudkip123

This isn't in my linear algebra textbook so I don't know how to do this...

5. Apr 4, 2012

micromass

Staff Emeritus
You have been given enough hints. We will only help you further if you make an attempt now.