Mark each statement true or false

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Reference no: EM1314286

Question: In the given problem, A is an n x n (square) matrix. Mark each statement True or False. Explain your answer.

If Ax = lambda x for some vector x, then lambda is an eigenvalue of A.
Finding an eigenvector of A may be difficult, but checking whether a given vector is in fact an eigenvector is easy.
To find the eigenvalues of A, reduce A to echelon form.
A number c is an eigenvalue of A if & only if the equation (A - cI)x = 0 has a non-trivial solution
A matrix A is not invertible if & only if 0 is an eigenvalue of A.

Reference no: EM1314286

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