Sum of all entries In a Matrix of Linear Transformation So,few days before I had a Linear Algebra Test and we had following question :
Let $P_3[R]$ denote the vector space of all polynomials with degree $\le 3$. Define the linear Transformation $P_3[R]$ $\to$ $P_3[R]$ defined by : 
$T(p(x))$ = $p(x)$ + $p'(x)$ + $p''(x)$ Then find the sum of all the matrix of T relative to the usual basis.
Now the basis for given vector space is :$\{1,x,x^2,x^3\}$ , Using this:
$T(1)$ =  $1$
$T(x)$ = $x$ + $1$ +$0$ = $1.1$ + $1.x$ + $0.x^2$ + $0.x^3$
$T(x^2$) = $x^2$ +  $2x$ + $2$  = $2.1$ + $2.x$ + $1.x^2$  + $0.x^3$
$T(x^3)$ = $x^3$ + $3x^2$ + $6x$ =  $0.1$ + $6.x$ + $3.x^2$ +  $1.x^3$
The Matrix is given by  :
$$
\begin{pmatrix}
1 & 1 & 2 & 0\\
0 & 1 & 2 & 6 \\
0 & 0 & 1 & 3\\
0 & 0 & 0 & 1\\
\end{pmatrix}$$
Clearly sum of all entries in the matrix is $18$ but the answer given to me is $24$
Can anyone tell me what is the error in my solution ?
Thank you.

In $$(1+x+x^2+x^3)+(1+2x+3x^2)+(2+6x),$$
the sum of the coefficients is $18$.
In $$(1+x+x^2+x^3)+(1+2x+3x^2)+(2+6x)+(6),$$
it is $24$.
