Suppose the linear transformation T P2P3 is defined as follo

Suppose the linear transformation T: P₂-->P₃ is defined as follows: T(p(t))=(a₀+a₁t+a₂t²)=(a₂-2a₁)t+(a₁-a₀)t³. Describe all of the vectors p(t) in the kernal of T.

Solution

T(p(t))=0 gives:

(a2-2a1)t+(a1-a0)t^3=0

a2-2a1=0

a1-a0=0

Hence, a2=2a1,a0=a1

So,

p(t)=a1(1+t+2t^2) are the vectors in kernel of T