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This assignment contains some TRUE or FALSE statements. For each statement you need to decide if it is true or not, and justify your answer. How to justify your answer. 0 In order to show that a statement is false, it sufces to give a counterexample. For example, consider the the statement: The last digit of every odd number is either I, 3, or '7. To show that this statement is false, it is enough to point out that, for example, 15 is an odd number, but its last digit is 5. a In order to show that a statement is true, you need to provide a reasoning explaining why it is true in all instances. Giving one example when it is true will not sufce, since the statement may not work in some other cases. For example, consider the statement: If n is an even number then u + 2 is also an even number. You can justify that this is true as follows. Even numbers are integers which are multiples of 2. If n is even then n : 2m for some integer m. Then [1 + 2 = 2m + 2 : 2(m + 1), which shows that n + 2 is even. (1) If A is a 3 X 5 matrix then rank(A) S 3. (2) The eigenvalues of a matrix are on its main diagonal (3) If A and B are 3 X 3 matrices, det(A)+det(B)=det(AB) (4) An invertible matrix is diagonalizable (5) A diagonalizable matrix is invertible (6) If B 2 b1, b2, b3 is an orthogonal basis of R3, and v in R3 is a vector orthogonal to both b1 and 1);, then v : cb3 for some scalar c