Find the matrices for change of basis in both directions between
the standard basis of R^{3} and the basis formed by the
columns of the matrix
Let f be the linear function from R^{3} to R^{3}
given by f(x) = M x where
Find the matrix of f relative to the basis of R^{3}
given by the columns of the matrix in the preceding exercise.
Let sigma denote reflection in the plane x + y + z = 0
(a linear function from R^{3} to R^{3}). Find the standard
matrix of sigma, i.e., the matrix of sigma relative to
the standard basis of R^{3}.