[Math] Rewriting matrix transformation as standard matrix

Question

I'm following a textbook chapter on matrix transformations, and one of the examples seems off.

Would this not actually be:

$$T\begin{pmatrix}\begin{bmatrix}x_1 \\ x_2\end{bmatrix}\end{pmatrix} = \begin{bmatrix} 3x_1+x_2 \\ 2x_1 – 4x_2\end{bmatrix} = \begin{bmatrix}3 && 1 \\ 2 && -4\end{bmatrix}\begin{bmatrix}x_1 \\ x_2\end{bmatrix}$$

Thus the standard matrix is $\begin{bmatrix}3 && 1 \\ 2 && -4\end{bmatrix}$?

I'm just unsure if it's perhaps a typo in the text or my understanding of the material is flawed. Take for example:

$$T(x_1,x_2,x_3) = (4x_1, 7x_2, -8x_3)$$

Would the standard matrix for $T$ be $\begin{bmatrix}4 && 0 && 0 \\ 0 && 7 && 0 \\ 0 && 0 && -8\end{bmatrix}$?

Answer 1

It is definitely a typo. Good job on spotting the flaw. [This posted as an answer instead of a comment so this post will not go unanswered.]