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Exercise 8.11.1

Avg difficulty 3.0

Find the (real or complex) eigenvalues and eigenvectors of the following matrices. Diagonalize each matrix if possible.

A=[21−12],B=[−1−211],C=[2−13011−110],D=[111−1201−11]A=\left[\begin{array}{rr}2&1\\ -1&2\\ \end{array}\right],\quad B=\left[\begin{array}{rr}-1&-2\\ 1&1\\ \end{array}\right],\quad C=\left[\begin{array}{rrr}2&-1&3\\ 0&1&1\\ -1&1&0\\ \end{array}\right],\quad D=\left[\begin{array}{rrr}1&1&1\\ -1&2&0\\ 1&-1&1\\ \end{array}\right]

Selinger, Matrix Theory and Linear Algebra, Eigenvalues, eigenvectors, and diagonalization, Complex eigenvalues and eigenvectors, Exercise 8.11.1

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.