## Invariant Lines

Any transformation represented by a matrix whose entries are numbers is linear. The matrix will send a line to a line. The transformed line will in general be rotated and scaled, but it will still be a line. For example, suppose a transformationis represented by the matrix Consider the effect ofon the lineThis may be represented by the vectorsendsto

Henceand

Rearranging the first of these givesSubstitute this into the second to obtain