Originally Posted by
shuaige 3) Let T: P2 --> R be the linear transformation defined by int [p(x)] from 0 to 1
a) (2) Find the ker(T)
b) (2) Find a basis for basis for ker(T).
for part a, what i did is:
p(x) = a+bx+cx^2
then, int [ a+bx+cx^2] from 0 to 1 and i got: a+b/2+c/3. then set this equation =0
now let a=s, b=t, therefore, c= -3s - 3/2 t
Thus, I conclude that Ker(t) = {(-3s - 3/2 t): where s and t are any real numbers}
Is this process correct?
to continue the problem, for part b
I just simply substitute a set of number, say s=0, t=1, i get -3/2, then is this the basis for the kernel? or did i miss anything there?
Thanks in advance