Let T : R3 → R3 be the linear transformation whose matrix with respect to standard basis {e1, e2, e3} of R3 is:
\(\left[ {\begin{array}{*{20}{c}} 0&0&1\\ 0&1&0\\ 1&0&0 \end{array}} \right]\).
Then T
1
maps the subspace spanned by e1 and e2 into itself
2
has distinct eigenvalues
3
has eigenvectors that span R3
4
has a non-zero null space