Find [v]s with Basis S={t+1,t-1} in P_1: v=5t-2"

  • Thread starter Thread starter hadizainud
  • Start date Start date
  • Tags Tags
    Basis
Join the discussion
Registration is free. Start your own thread to ask a follow-up.
5 replies · 2K views
hadizainud
Messages
15
Reaction score
0

Homework Statement



Let v=5t-2,S={v_1,v_2 }={t+1,t-1} is a basis of P_1 where P_1 is a vector space of all polynomials of degree ≤1. What is [v]s? Let v=5t-2,S={v_1,v_2 }={t+1,t-1} is a basis of P_1 where P_1 is a vector space of all polynomials of degree ≤1. What is [v]s?

2. The attempt at a solution
I need your help to provide me the correct way of putting the answers together, like the one in the answer scheme. Thanks in advance!
 
Physics news on Phys.org
You need to show some attempt at doing the problem yourself before receiving help here.
 
v=[5t-2]=a[t+1]+b[t-1]

(1st) at+bt=5t
(2nd) a-b=-2
v=3⁄2 v_1+7⁄2 v_2
[v]_s=[■(3⁄2@7⁄2)]
is this correct?
 
hadizainud said:
v=[5t-2]=a[t+1]+b[t-1]

(1st) at+bt=5t
(2nd) a-b=-2
v=3⁄2 v_1+7⁄2 v_2
Looks good. I'm not exactly sure what the following notation means, though:
[v]_s=[■(3⁄2@7⁄2)]
is this correct?
 
What about those of us who do not use "Microsoft Word Office"?