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**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