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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 single blank.) A = 0 −1 −1 0 (reflection in the line y = −x)

Respuesta :

mavila18

Answer:

[tex]v_1=(1,1)\\v_2=(-1,1)[/tex]

Step-by-step explanation:

you have the matrix

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

to find the eigenvalues it is necessary to solve the determinant

[tex]|A-\lambda I|=0\\[/tex]

thus, we have the polynomial and the eigenvalues

[tex]\lambda ^2-1=0\\\lambda_1=1\\\lambda_2=-1[/tex]

and the eigenvectors

[tex]v_1=(1,1)\\v_2=(-1,1)[/tex]

Hope this helps!

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