Maple - linear transformation - parametric equation

Question

I have the line $l = \begin{cases} x=-2t+1 \\ y=3t-2 \\ z=t+4 \end{cases} $ and a linear transformation $T$ and I want to find a parametric equation of the line $l^*$ so that $l^*$ is the image of the line $l$ under $T\\ \\$ $\\$ ($T: l\rightarrow l^*\\$) Is the general approach or function to solve this kind of problem using Maple 18? Thanks in advance!

Answer 1

Write your line in the form $$ \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} l\\m\\n\end{bmatrix} t + \begin{bmatrix} x_0 \\ y_0 \\ z_0\end{bmatrix}.$$ The equations you are looking for are the following: $$ \begin{bmatrix} x' \\ y' \\ z'\end{bmatrix} = T\begin{bmatrix} x \\ y \\ z \end{bmatrix}=T\left(\begin{bmatrix} l\\m\\n\end{bmatrix} t + \begin{bmatrix} x_0 \\ y_0 \\ z_0\end{bmatrix}\right), $$ so you just need to compute a product of the matrix $T$ times a vector, and this can be done with the dot . in the LinearAlgebra package.