Find EIGENVALUES and EIGENVECTORS for the matrix The

Find EIGENVALUES and EIGENVECTORS for the matrix:

The EIGENVALUES are 2 and -1

The NULL SPACE of contains solutions to: The EIENVECTORS belonging to 2 are nonzero multiples of

The NULL SPACE of contains solutions to: The EIENVECTORS belonging to -1 are nonzero multiples of

has EIGENVALUES : 2 and EIGENVECTORS: Cosets of eigenspace? ? -1

has EIGENVALUES : 2 and EIGENVECTORS: Consider the EIGENSPACE W = -1

Consider the EIGENSPACE W = W Add the same vector to every point on W to get a COSET OF W

Consider the EIGENSPACE W = W Add the same vector to every point on W to get a COSET OF W - a line parallel to W

Consider the EIGENSPACE W = W The COSETS of the EIGENSPACE W are lines parallel to W.

Consider the EIGENSPACE W = W The blue coset can be obtained by adding the vector to each vector in W

Consider the EIGENSPACE W = W The blue coset can be obtained by adding the vector to each vector in W

Consider the EIGENSPACE W = If v is a vector in the blue coset then v = k W + The blue coset can be obtained by adding the vector to each vector in W

Consider the EIGENSPACE W = If v is a vector in the blue coset then v = k + v W

Consider the EIGENSPACE W = If v is a vector in the blue coset then v = k W + Av = k. A + A vector on W A

Consider the EIGENSPACE W = If v is a vector in the blue coset then v = k W + Every point on the blue coset has an image on the green coset. Av = k. A + A vector on W A

Consider the EIGENSPACE W = If v is a vector in the blue coset then W v = k + Av = k. A + A A vector on W If B is a coset of an eigenspace W then A maps every point on B onto G , another coset of W.