Let \(T\left( \begin{bmatrix} x_1 \\ x_2\end{bmatrix}\right) =
\begin{bmatrix}
x_1 + x_2 \\
2x_1
\end{bmatrix}\).
What is the second component of
\(T\left(T\left(\begin{bmatrix} 0 \\ 1\end{bmatrix}\right)\right)\)?
The answer is 2.
Note that
\(T\left(\begin{bmatrix} 0 \\ 1\end{bmatrix}\right)
= \begin{bmatrix} 0 + 1\\ 2(0)\end{bmatrix}
= \begin{bmatrix} 1\\ 0\end{bmatrix}
\).
Hence,
\(T\left(T\left(\begin{bmatrix} 0 \\ 1\end{bmatrix}\right)\right)=
T\left(\begin{bmatrix} 1 \\ 0\end{bmatrix}\right)
= \begin{bmatrix} 1+0\\ 2(1)\end{bmatrix}
= \begin{bmatrix} 1\\ 2\end{bmatrix}.\)
The second component of
\(\begin{bmatrix} 1\\ 2\end{bmatrix}\) is 2.