Hi.

A transformation : is represented by the matrix .

There is a line through the origin for which every point is mapped onto itself under .

Find the cartesian equation of this line.

I have already worked out the two eigenvalues for this matrix, 1 and -6.

Forming the equation:

Where are my respective eigenvalues.

The question I have is which on do I use, using 1 I get and using -6 I get .

My answers tell me that;

So 1 is the value I should use, but what exactly does the above expression mean?is associated with point invariant line

Thanks in advance