Please help me to answer the question below in detail. I really don't understand it. Thank you so much, and have a great day!

Label each of the following statements as true or false. If true, prove the statement. If false, provide a counterexample. If proof or counterexample is not provided, you will receive 0 points on the exercise. (a) A vector is an nrtuple of real numbers. (b) Every linear transformation has innitely many complex eigenveetors associated with it. (c) An example of an inner product on P" is (p,q} :2 I: p2(2:)q2(a:)d:c where 33,19 6 P... ((1) Elementary matrices are diagonalizable. (e) Every element of P2 can be written as the sum of p + q, where p 6 S, a proper subspace of P2 and q is in the orthogonal complement of S