Problem 6. (5 points. ) Mark the following as true or false. Very briefly explain your answers. t+1 -5 1. For any real number t , the matrix A = is always invertible. 2 t+1 2. If A is a 4 x 4 invertible matrix such that A' +3A = 0 , then det(A) > 50 . Note: O is the 4 x 4 zeromatrix. 3. If p, q,r are three 3 x 1 column vectors such that p = 7q + 3r , then det pq r] = 21 , where [par] is a 3 x 3 matrix consisting of p,q,r as its columns. 4. The permutation o of 12 numbers given by o = (4, 2, 11, 8, 5, 1, 12, 7, 10, 3, 6,9) has a negative signature. 5. As part of the definition of defining a vectorspace V , the statement "for any vector xEV , we have 0 =0v " is one of the vectorspace axioms, where Ov is the zerovector of V