Let $\mathrm{S}=\{4,6,9\}\text{ and }\mathrm{T}=\{9,10,11,\dots ,1000\}$. If $\mathrm{A}=\left\{{\mathrm{a}}_1+{\mathrm{a}}_2+\dots +{\mathrm{a}}_{\mathrm{k}}:\mathrm{k}\in \mathrm{N},{\mathrm{a}}_1,{\mathrm{a}}_2,{\mathrm{a}}_3,\dots ,{\mathrm{a}}_{\mathrm{k}}\in \mathrm{S}\right\}$, then the sum of all the elements in the set T-A is equal to______.

$\mathrm{S}=\{4,6,9\},\mathrm{T}=\{9,10,11,\dots 1000\}$
$\begin{array}{l}\mathrm{A}=\left\{{\mathrm{a}}_1+{\mathrm{a}}_2+\dots \dots .{\mathrm{a}}_{\mathrm{k}}:\mathrm{k}\in \mathrm{N},{\mathrm{a}}_1,{\mathrm{a}}_2,\dots ,{\mathrm{a}}_{\mathrm{k}}\in \mathrm{S}\right\}\\ \Rightarrow \mathrm{A}=\{\mathrm{a}:\mathrm{a}=4\mathrm{x}+6\mathrm{y}+9\mathrm{z}\}\end{array}$
Except the element 11, every element of set T is of the form $4\mathrm{x}+6\mathrm{y}+9\mathrm{z}$ for some  $\mathrm{x},\mathrm{y},\mathrm{z}\in \mathrm{W}\therefore \mathrm{T}-\mathrm{A}=\left\{11\right\}$
$\therefore \text{ Sum of all element in }\mathrm{T}-\mathrm{A}=11$