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Decide if each of the following statements are true or false. If a statement is true,...

Decide if each of the following statements are true or false. If a statement is true, explain why it is true. If the statement is false, give an example showing that it is false.

(a) Let A be an n x n matrix. One root of its characteristic polynomial is 4. The dimension of the eigenspace corresponding to the eigenvalue 4 is at least 1.

(b) Let A be an n x n matrix. A is not invertible if and only if 0 is one of its eigenvalues (Hint: Review the Invertible Matrix Theorem)

(c) A 2 x 2 matrix must have two distinct eigenvalues.

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