1.1.28. d - c(b/a) not equal 0, or ad-bc not equal 0. 1.4.14. No. The equation Ax=u has no solution. 1.4.18. Only 3 rows contains a pivot position. The equation Bx=y does not have a solution for each y in R^4, by Thm 4. 1.4.24. TTTTFT. 1.5.10. x = x_2 (-3,1,0,0,) + x_3 (0,0,1,0) + x_4 (4,0,0,1) 1.5.30. a yes, b no. 1.5.32. a yes, b yes. 1.6.12. a x_1 = 100 + x_3 - x_5 x_2 = 100 - x_3 + x_5 x_3 = free x_4 = 60 - x_5 x_5 = free b min value of x_1 is 40. 1.7.2. lin indep. 1.7.28. It must have 5 pivot columns. 1.9.2. [1 4 -5] [3 -7 4] 1.9.10. [0 -1] [-1 0] 2.1.8. B has 3 rows. 2.1.10. AB = AC = [1 -7 ] [-2 14] 2.2.6. x_1=2 and x_2=5 2.2.32. Not invertible. 2.3.24. Eqn Lx=0 always has the trivial solution. This fact gives no information about the cols of L. 2.5.2. Ly=b gives y=(2,-2,2), Ux=y gives x=(1/4,2,1). 3.1.8. -11 3.1.10. -6. Start with row 2. 3.1.12. 36. Start with row 1 or col 4. 3.2.6. -18. 3.2.16. 21. 3.2.22. Not invertible. 3.2.24. Lin indep.