A First Course in Linear Algebra · Problem C21

Eigenvalues — Robert Beezer

Mathematics — Linear Algebra · geometric-multiplicity

Problem

The matrix

A

below has

\lambda = 2

as an eigenvalue. Find the geometric multiplicity of

\lambda = 2

using your calculator only for row-reducing matrices.

A = \begin{bmatrix} 18 & -15 & 33 & -15 \\ -4 & 8 & -6 & 6 \\ -9 & 9 & -16 & 9 \\ 5 & -6 & 9 & -4 \end{bmatrix}