Suppose a 3 x 3 real matrix A has only two (real) distinct eigenvalues. Suppose that...

Transcribed Image Text:

Suppose a 3 x 3 real matrix A has only two (real) distinct eigenvalues. Suppose that tr(A) = -4 and det(A) = smaller eigenvalue = larger eigenvalue = has multiplicity | has mulitiplicity and -32. Find the eigenvalues of A with their algebraic multiplicities. 11 21 Let M = Find formulas for the entries of M", where n is a positive integer. MT= [1 5 5 Let A = 0 4 3 0 -2 x = Find an invertible matrix X and a diagonal matrix D such that D = X-AX. D = Hint: The eigenvalues are 2, 1 and 1. Suppose a 3 x 3 real matrix A has only two (real) distinct eigenvalues. Suppose that tr(A) = -4 and det(A) = smaller eigenvalue = larger eigenvalue = has multiplicity | has mulitiplicity and -32. Find the eigenvalues of A with their algebraic multiplicities. 11 21 Let M = Find formulas for the entries of M", where n is a positive integer. MT= [1 5 5 Let A = 0 4 3 0 -2 x = Find an invertible matrix X and a diagonal matrix D such that D = X-AX. D = Hint: The eigenvalues are 2, 1 and 1.