Question: Suppose a 3 x 3 real matrix A has only two (real) distinct eigenvalues. Suppose that tr(A) = -4 and det(A) = -32. Find the

Suppose a 3 x 3 real matrix A has only two (real) distinct eigenvalues. Suppose that tr(A) = -4 and det(A) = -32. Find the eigenvalues of A with their algebraic multiplicities. smaller eigenvalue =

has mulitiplicity and larger eigenvalue = has mulitiplicity11 2 Let M =

5 Find formulas for the entries of M" where n is a

Suppose a 3 x 3 real matrix A has only two (real) distinct eigenvalues. Suppose that tr(A) = -4 and det(A) = -32. Find the eigenvalues of A with their algebraic multiplicities. smaller eigenvalue = has mulitiplicity and larger eigenvalue = has mulitiplicity11 2 Let M = 5 Find formulas for the entries of M" where n is a positive integer. M" = 18215 CT Let A = 0 4 3 Find an invertible matrix X and a diagonal matrix D such that D = X-AX. -1 X = , D = Hint: The eigenvalues are 2, 1 and 1

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