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note eigenvector cannot be zero eigenvalue canbe 0 suppose 0 eigenvalue
Note that an eigenvector cannot be zero, but an eigenvalue canbe 0. Suppose that 0 is an eigenvalue of A. What does it say about A? (Hint: One of themost important properties of a matrix is whether or not it is invertible. Think about theInvertible Matrix Theorem and all the ‘good things’ of dealing with invertible matrices)