0 -1 2 A = 2 1 1 -1 3 -4

Find the eigenvalues and eigenvectors for the coefficient matrix.

Find the eigenvalues and a basis for for the eigenspace of the matrix associated with each -2 2 eigenvalue for B = 0 0 0

Let A be a arbitrary n x n matrix, Show that if A1 and A2 are two eigenvalues with A1 # ^2 and eigenvectors vi and v2, respectively. Show that vị and v2 are linerly independent.