4. Let V be a vector space over C and let T : V → V be a linear transformation. (a) State the definition of an eigenvector of T. (b) If 0 is an eigenvalue of T, show that T is not invertible. (c) Find the eigenvectors and eigenvalues of the matrix A given below. -1 0 0 A = 10 3 1 6 0 2

Q: 5. The number 0 can never be an eigenvalue of a linear operator. True or False?

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