Transcription of Chapter 1 Solutions to Review Problems
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Chapter 1 Solutions to Review Problems
Chapter 1 Solutions to Review ProblemsChapter 1 Exercise 42 Which of the following equations are not linear and why:(a)x21+ 3x2 2x3= 5.(b)x1+x1x2+ 2x3= 1.(c)x1+2x2+x3= (a) The given equation is linear by (??).(b) The equation is not linear because of the termx1x2.(c) The equation is nonlinear becausex2has a negative powerExercise 43 Show that(2s+ 12t+ 13, s, s 3t 3, t)is a solution to the system{2x1+ 5x2+ 9x3+ 3x4= 1x1+ 2x2+ 4x3= these values forx1, x2, x3,andx4in each + 5x2+ 9x3+ 3x4= 2(2s+ 12t+ 13) + 5s+ 9( s 3t 3) + 3t= 1x1+ 2x2+ 4x3=(2s+ 12t+ 13) + 2s+ 4( s 3t 3)= both equations are satisfied, then it is a solution for allsandt12 Chapter 1. Solutions TO Review PROBLEMSE xercise 44 Solve each of the following systems using the method of elimination:(a){4x1 3x2= 02x1+ 3x2= 18(b){4x1 6x2= 106x1 9x2= 15(c){2x1+x2= 32x1+x2= 1 Which of the above systems is consistent and which is inconsistent?Solution.(a) Adding the two equations to obtain 6x1= 18 orx1= value forx1in one of the given equations and then solving forx2we findx2= system is consistent.}}}}
2 CHAPTER 1. SOLUTIONS TO REVIEW PROBLEMS Exercise 44 Solve each of the following systems using the method of elimination: (a) ˆ 4x 1 −3x 2 = 0 2x 1 +3x 2 = 18 (b) ˆ 4x
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