9. Let T: R2 -> R2
be defined by
Which of the following is an equation of the line
that is mapped onto itself by T?
| A. y-x = 0 | B. 2 x + y = 0 | C.-x+4y = 0 | D. x + 2 y = 0 | E. 4 x - y = 0 |
Solution. The answer is A.
Eigenvectors can be considered as lines mapped
onto themselves by T.
Consider
This says that 3 is the only eigenvalue. The corresponding equation for the eigenvectors is
Consequently the eigenvectors have y = x. That is, the line y = x is mapped onto itself by T.