91Ó°ÊÓ

\(\operatorname{For} A=\left[\begin{array}{ccc}{1} & {2} & {3} \\ {1} & {2} & {3} \\ {1} & {2} & {3}\end{array}\right],\) find one eigenvalue, with no calculation. Justify your answer.

It can be shown that the trace of a matrix \(A\) equals the sum of the eigenvalues of \(A .\) Verify this statement for the case when \(A\) is diagonalizable.

In Exercises 31 and \(32,\) let \(A\) be the matrix of the linear transformation \(T .\) Without writing \(A\) , find an eigenvalue of \(A\) and describe the eigenspace. \(T\) is the transformation on \(\mathbb{R}^{2}\) that reflects points across some line through the origin.