I have a 4×4 matrix with entries R1 (1,1,0,0) R2 (2,2,0,0) R3(0,0,3,0) R4(0,0,5,5).question is to find the no. of independent eigenvectors.I calculate eigenvalues as 0,5,3,3 nd then geometric multiplicity of eigenvalue 3 as 2.so my answer was 4.but I am getting wrong. Pls help.
about eigenvectors
-1
$\begingroup$
eigenvalues-eigenvectors
-
0Why do you think it's wrong? – 2017-02-10
1 Answers
0
The four independent eigenvectors are $$\begin{bmatrix}1\\ -1 \\ 0\\ 0\end{bmatrix},\begin{bmatrix}1\\2\\0\\0\end{bmatrix},\begin{bmatrix}0\\0\\2\\-5\end{bmatrix}\text{ and }\begin{bmatrix}0\\0\\0\\1\end{bmatrix},$$ corresponding to the eigenvalues $0,3,3\text{ and }5$ respectively. You can verify them.