Consider the following statements: 1. If A is a square matrix and Av = λv, for some nonzero number λ, then v is an eigenvector of A. 2. If λ is an eigenvalue of a square matrix A of order n, then the homogeneous linear system (A−λIn)x = 0 has infinite solutions. 3. The characteristic polynomial p(λ) of a square matrix A, of order n, has degree n and its real roots are eigenvalues ​​of A. 4. If λ is an eigenvalue of a square matrix A, then the set of eigenvectors of A associated with λ is a vector space.   Choose an option: (a) Statements 2 and 3 are true (b) Statements 1, 2, 3 and 4 are false. (c) Statements 1, 2 and 3 are true. (d) Only statements 2 and 4 are false. (e) All statements are true.

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