1. If a 3 x 3 matrix A has det( A) - -1, find det (; A), det(-A), det(A?), and det(AT!). 2. Suppose that A is an n x n matrix where the entries of each row sum to zero. What is the value of det (A)? Justify your answer. 3. Let N - (a) Is the vector 1 = contained in Span ( 71, 62, 63, WA }? If so, write u as a linear combination 1 - and + aziz + 0ads + and using as few non-zero scalars for a1, a2, a3, 4 as possible. (b) Is the vector wi contained in Span( 61, 52, 73, 71}7 If so, write a as a linear combination w - biv1 + 6202 + bus + bus using as few non-zero scalars for 41, 02, 43, 41 as possible. 4. Find the largest possible number of linearly independent vectors among In other words, what's the size of the largest linearly independent set formed from the vectors above? Justify your answer. 5. Let {11, u2, us } be a set of linearly independent vectors, and define the following vectors. 71 - 12 + 13, 12 - u1 + 13, 13 - 11 + 12 1 - 12 - 13, 12 - 11 - 13. w3 - 1 - uz (a) Determine whether { 61, 72, 53 } are linearly independent or dependent. (b) Determine whether { 1/1, w/2, w3} are linearly independent or dependent