Hi
can someone explain to be how they get the eigenvectors for the following matrix
hence
eigenvalues are
i get
however answers says when
matrix is
i don't understand how they got this result, someone please explain this to me.
P.S
Hi
can someone explain to be how they get the eigenvectors for the following matrix
hence
eigenvalues are
i get
however answers says when
matrix is
i don't understand how they got this result, someone please explain this to me.
P.S
You are making two errors. The first is in thinking that the row reduced matrix leads to . This really the reduced form of the "augmented matrix"
for solving the matrix equation .
That is, it corresponds to the equation so that you get , not .
Your second error is in thinking you can set v2= 1 to get (using the correct ) and then set to get . You can do one or other, not both! If you set v2= 1, you get v1= 1/2 and so have the eigenvector . If you take v1= 1, you get v2= 2 and so have the eigenvector .
Since one is a multiple of the other, both are eigenvectors corresponding to eigenvalue 4.