Question

The effect of the linear transformation T:R^2 to R^2 with matrix \[A=\left[\begin{matrix}1&0\\0&-1\end{matrix}\right]\] is to reflect each vector in the x-axis. By arguing geometrically, determine all eigenvalues and eigenvectors of A
Please, help

Answer 1

@dumbcow

Answer 2

@dan815

Answer 3

no algebraic way, just geometric arguing, dan

Answer 4

@Loser66 , linear algebra...arguing geometrically....sorry im out :P

Answer 5

ok, thanks for reply anyway

Answer 6

dan 1.0 reflect to itself

Answer 7

so the eigenvalue is 1

Answer 8

right?

Answer 9

oh i see u mean that is the matrix that does the roration

Answer 10

we have to argue for eigenvalue and eigenvectors, I think about the eigenvalues only. because eigenvectors belong to them

Answer 11

thereforre only the y compoentnts will be effected by a switch of -1