Determine whether the mapping T is a linear transformation and if so find its kernel. T:P2->P2,...

 

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Determine whether the mapping T is a linear transformation and if so find its kernel. T:P2->P2, where a) T(a0+a1x+a2x^2)=a0+a1(x+1)+a2(x+1)^2 b)T(a0+a1x+a2x^2)=(a0+1)+(a1+1)x+(a2+1)x^2. show T(ku)=kT(u) and T(u+v)-T(u)+T(v) but I/m not sure how to do that. Determine whether the mapping T is a linear transformation and if so find its kernel. T:P2->P2, where a) T(a0+a1x+a2x^2)=a0+a1(x+1)+a2(x+1)^2 b)T(a0+a1x+a2x^2)=(a0+1)+(a1+1)x+(a2+1)x^2. show T(ku)=kT(u) and T(u+v)-T(u)+T(v) but I/m not sure how to do that.