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Matrix and eigenvalues

Please see the attached Word document.
Thank-you for your help.

Suppose that A is a square matrix, and that the only eigenvectors of A are scalar multiples of the vector:

Deduce as much information as you can about A, by answering the following questions. Give reasons for your answers.

(a) What size is A?

(b) How many eigenvalues does A have? Can you tell what the eigenvalues are?

(c) What can you tell about the algebraic and geometric multiplicities?

(d) Can you tell whether or not A is diagonalizable?


Solution Summary

This provides examples of working with a matrix regarding eigenvalues, diagonalizability, and multiplicities.