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3.3 Exercises Use Cramer's rule to compute the solutions of the systems in 9. sx1 + 2sx2 =-1 10. SXI - 2x2 = 1 Exercises 1-6. 3x1 + 65x2 = 4 4sx1 + 45x2 = 2 1. 5x1 + 7x2 = 3 2. 4x1+ X2= 6 2x1 + 4x2 = 1 3x1 + 2x2 = 5 In Exercises 11-16, compute the adjugate of the given matrix, and then use Theorem 8 to give the inverse of the matrix. 3. 3x1 - 2x2 = 3 4. -5x1 + 2x2 = 9 O - W -4x1 + 6x2 = -5 3x1 - X2 =-4 11. N O 12. ON 5. XI + X2 = 3 6. x1 + 3x2+ X3=8 -3X1 + 2x3 = 0 -X'1 + 2X3 = 4 w -1 X2 - 2X3 = 2 3x1+ X2 = 4 O - 13. 14. aFN ON N In Exercises 7-10, determine the values of the parameter s for which the system has a unique solution, and describe the solution. . un 7. 6sx1 + 4x2 = 5 8. 3sx1 + 5x2 = 3 15. -1 OWN WHO HOO 16. N - A O 9x1 + 25x2 = -2 12x1 + 5sx2 = 2 OIn Exercises 19-22, find the area of the parallelogram whose vertices are listed. 19. 20, 21. 22. 23. 24, 25, 26. (0,0), (5,2), (6,4), (11,6) (0,00, (~2, 4), 6, 5), 4, ~1) (=2, 0, 0, 3, {30, (1.4 (0,2), (52, (3,1, 2, 13 Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1,0,-3), (1,2,4), and 3.1, U, Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1,3,0), (2,0,2), and (1,3,1). Use the concept of volume to explain why the determinant of a 3 x 3 matrix A is zero if and only if A is not invertible. Do not appeal to Theorem 4 in Section 3.2, [Hint: Think about the columns of A.] Let 7. R R\" be a linear transformation, and let p be a vector and 5 a set in R"'. Show that the image of p + S under 1" is the translated set 7'(p) 4+ 7(S) in R&quot