Let T P4P3 be a linear transformation given by Tpp WHat is t

Let T: P₄--->P₃ be a linear transformation given by T(p)=p\'. WHat is the kernel of T?

Solution

Given that T is a linear transformation from P4 to P3.

Let P4 be a0+a1x+a2x²+a3x³

T(p) = p\' = a1+2a2x+3a3x²

T(P) would be 0 if a1, a2 and a3 are 0

Hence If P(X) = a0 then

T(P) = p\'=0

So kernel of T is the constant

P(x) = a0 (without x terms)