Show that if A is a matrix and 1, 2, ..., k are distinct eigenvalues with associated eigenvectors x1, x2, ..., xk, then {x1, x2,

Show that if A is a matrix and λ1, λ2, ..., λk are distinct eigenvalues with associated eigenvectors x1, x2, ..., xk, then {x1, x2, . . . , xk} is a linearly independent set.