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

[hadizainud]

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!

 

[vela]

You need to show some attempt at doing the problem yourself before receiving help here.

 

[hadizainud]

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?

 

[vela]

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?

 

[hadizainud]

I'm doing the answers of my tutorial on Microsoft Word Office.
If you paste what I've wrote there in Equation box, you should see it come.
Anyway, thanks man :)
I got a new thread on Physicsforums - https://www.physicsforums.com/showthread.php?p=3448198

 

[HallsofIvy]

What about those of us who do not use "Microsoft Word Office"?