Let T P2 rightarrow P2 be the mapping defined by Ta0 a1x a

Let T: P_2 rightarrow P_2 be the mapping defined by T(a_0 + a_1x + a_2x^2) = 2a_0 + (a_0 + a_1) x+ a_1x. Show that T is a linear transformation.

Solution

1.T(0+0x+0x^2)=2*0+0x+0x=0

2. T(a0+a1x+a2x^2+b0+b1x+b2x^2)=T((a0+b0)+(a1+b1)x+(a2+b2)x^2)

                            =2(a0+b0)+(a0+b0+a1+b1)x+(a1+b1)x=2a0+(a0+a1)x+a1x+2b0+(b0+b1)x+b1x

Hence , T is a linear transformation.