Suppose a 3 x 3 real matrix A has only two (real) distinct eigenvalues. Suppose that tr(A) = -1 and det(A) = 112. Find the eigenvalues of A with their algebraic multiplicities. smaller eigenvalue = has multiplicity and larger eigenvalue = has multiplicity

Find all of the eigenvalues of the matrix A over the complex numbers C. Give bases for each of the corresponding eigenspaces. A = 4-1-1 = 1+i has eigenspace span has eigenspace span × !- (2-value with smaller imaginary part) (2-value with larger imaginary part)

Suppose A is a 3 x 3 matrix with eigenvectors [1] V1 = V2 = 1 and v3 = corresponding to eigenvalues A1 =-, d2 = }, and A3 = 1, respectively. Find A and A20.

Find a 2x2 matrix A that has two eigenvalues 4, -1 whose eigenvectors 2 and 1 are