SOLUTION: Show that the set S ={ t^2 +1, t - 1, 2t+2} forms a basis of P^2.

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Question 3813: Show that the set S ={ t^2 +1, t - 1, 2t+2} forms a basis of P^2.
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
a(t^2 +1)+ b (t - 1) + c( 2t+2 ) = 0
--> a t^2 + (b+2c)t + a-b +2 c = 0
--> a = 0 (since {t^2, t ,1} is the standard basis of P^2 )
b+2c = 0
a-b+2c = 0
--> a = b = c =0
This shows t^2 +1, t - 1, 2t+2 are independent and so
{ t^2 +1, t - 1, 2t+2} is a basis of P2 with dim 3.
Kenny