Show that the 5 × 5 matrix has an eigenvalue of

Chapter 8, Problem 31E

(choose chapter or problem)

Show that the 5 x 5 matrix

\(\mathbf{A}=\left(\begin{array}{lllll}

2 & 1 & 0 & 0 & 0 \\

0 & 2 & 0 & 0 & 0 \\

0 & 0 & 2 & 0 & 0 \\

0 & 0 & 0 & 2 & 1 \\

0 & 0 & 0 & 0 & 2

\end{array}\right)

\)

has an eigenvalue \(\lambda_{1}\) of multiplicity 5. Show that three linearly independent eigenvectors corresponding to \(\lambda_{1}\) can be found.

Text Transcription:

mathbf A =({array} lllll 2 & 1 & 0 & 0 & 0 0 & 2 & 0 & 0 & 0 0 & 0 & 2 & 0 & 0 0 & 0 & 0 & 2 & 1 0 & 0 & 0 & 0 & 2 {array})

lambda_1