# Invariant lines?

1. Jun 15, 2009

### Gregg

1. The problem statement, all variables and given/known data

find in the form y= mx+c, the invariant lines of the tranformation with matrix

$\left( \begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array} \right)$

$\left( \begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array} \right)\left( \begin{array}{c} x \\ \text{mx}+c \end{array} \right)=\left( \begin{array}{c} \text{mx}+c \\ x \end{array} \right)$

$\Rightarrow x = m(mx+c)+c$ Why???

I just don't understand how that is implied in the first place and I don't have a method of working out invariant lines in the form mx or mx+c!

2. Jun 15, 2009

### rock.freak667

Because you want a line whose x value will remain the same after undergoing the transformation.

So when you multiply the matrix by (x,y) you get (y,x). You then want your line to have the the x value of the 'old y value'

and if Y=MX+C

X= mx+c

so Y=M(mx+c) + C

(I used capital letters to explain it better even though, the capitals are the same as the common ones)