Exercise9

For each of the following matrix transformations, describe the eigenvalues and eigenvectors of the corresponding matrix \(A\text{.}\)

  1. A reflection in \(\real^2\) in the line \(y=x\text{.}\)

  2. A \(180^\circ\) rotation in \(\real^2\text{.}\)

  3. A \(180^\circ\) rotation in \(\real^3\) about the \(y\)-axis.

  4. A \(90^\circ\) rotation in \(\real^3\) about the \(x\)-axis.

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