MODULE 3 ASSIGNMENT 1. Let A = 4 3 Use expansion by cofactors down the 3rd column to find [A], the 1 1 2 determinant of A. 2. Using the results of question 1 only calculate |AT|, |A²|, |AAT|, |2A|, and |A¯¹|. 3. Solve for x in the determinant equation 2- X 1 3 = 0. -X 4. Use elementary row or column operations to evaluate the following determinant: 9-4 5 -5 -2 0 4 10 262 713 1241 5. Find the adjoint of the matrix A. Then use the adjoint to find the inverse of A, if possible, where [12 3 A = 01 −1 2 2 2 6. Use a determinant to find an equation of the plane through the points (1, −2, 1), (−1, −1, 7), (2, −1, 3). 7. Find the characteristic polynomial and the eigenvalues of A = 1