I'm trying to understand why is the following statement is true.
$\newcommand\V[3]{\begin{bmatrix}#1\\ #2\\ #3\end{bmatrix}}$ If $T\V100 = \V{a_1}{a_2}{a_3}$, $T\V110 = \V{b_1}{b_2}{b_3}$, and $T\V101 = \V{c_1}{c_2}{c_3}$, then $A = \begin{bmatrix}a_1 & b_1-a_1 & c_1-a_1 \\ a_2 & b_2-a_2 & c_2-a_2 \\ a_3 & b_3-a_3 & c_3-a_3\end{bmatrix}$.
Can someone help me please?