Question : eigenvectors

Hi

I'm trying to learn about eigenvectors and I don't understand my book.

To get the enigenvectors for this matrix  
4     1
3     2

You get a characteristic equation

| 4-lamba     1            |    = 0
| 3               2-lamba  |

lambda = 1 or 5

So you get whats below where the brackets indicate subscripts and the terms should be matrices

4     1     times         x(1)    =    1 times   x(1)
3      2                      x(2)                        x(2)

To get

4x(1) + x(2) = x(1)
3x(1) + 2x(2) = x(2)

Either of these gives x(2) = -3x(1)

It then says that 'this result tells us that whatever the value of x(1) is the x(2) is -3 times it and the eigenvector is

k
-3k

Why isn't it that x(2) is -3 times smaller than x(1) to give

k
k/-3

many thanks

Answer : eigenvectors

4     1     times         k    =    1 times   k
3      2                    -3k                     -3k