Find the eigenvalues and eigenvectors of A geometrically over the real numbers ℝ. (If an eigenvalue does not exist, enter DNE. If an eigenvector does not exist, enter DNE in any…

Question

asked Oct 21, 2021 155k views

1 Answer

Semsem · Answer 1 · 2021-10-27T22:03:40+0000

Answer:

$v_1=(1,1)\\v_2=(-1,1)$

Explanation:

you have the matrix

$A=\left[\begin{array}{cc}0&-1\\-1&0\end{array}\right]$

to find the eigenvalues it is necessary to solve the determinant

$|A-\lambda I|=0\\$

thus, we have the polynomial and the eigenvalues

$\lambda ^2-1=0\\\lambda_1=1\\\lambda_2=-1$

and the eigenvectors

$v_1=(1,1)\\v_2=(-1,1)$

Hope this helps!