Question

Find equations of the lines that map to themselves under the following transformation ...

Answer 1

\[\left[\begin{matrix}2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix}\right]\left(\begin{matrix}x \\ y \\ z\end{matrix}\right) = \left(\begin{matrix}X \\ Y \\ Z\end{matrix}\right)\]

Answer 2

Not sure the approache here; is it best to start from
\[(x-a)/b = (y-c)/d = (z-e)/f\] and pick coordinates that are transformed
for e.g. (a,b,c) maps to (2a,b,2z)

Answer 3

and go from there?

Answer 4

2x=X
y=Y
z=Z

Answer 5

apologies that bottom right parameter should be 2

Answer 6

then, 2z=Z :)

Answer 7

2x=X
y=Y
2z=Z
is the image of x,y,x
but how do you figure out the equation of the line that that maps to itself

Answer 8

so for example i can see that the y axis is 'invariant' i.e. doesnt change so x=0,z=0 would be one of the correct answers
for eg.
0,5,0 => 0,5,0

Answer 9

there is more than one answer, and i'd like to see the technique used