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Question: linear algebra number 391113...

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Linear algebra number #3,9,11,13
1.1 EXERCISES Solve each system in Exercises 1-4 by using elementary row operations on the equations or on the augmented matrix. Follow the systematic elimination procedure described in this section. 12. 3x +4x4 3x1 7x2 + 7x--8 x1 + 5x2 = 7 2. 2x1 + 4x2=-4 5x1 +7x21 2x1 + 2x2 +90-7 x2 + 5x2 3. Find the point (x,22) that lies on the line x + 5-7and on the line x1-2x2-2. See the figure. x2 x1-2x2-2 +5x7 14. xI-3x2 4. Find the point of intersection of the lines x 5x 1 and Determine if the systems in Exercises Do not completely solve the systems. Consider each matrix in Exercises 5 and 6 as the augmented matrix of a linear system. State in words the next two elementary row operations that should be performed in the process of solving the system. 15. 3x2 3.x 0 1-3 0 6 5. 16. xi 0 0 01 -5 2x2 + 2x3 =0 1-6 4 0 1 0 2 -7 0 0 0 1 2 -3 6. -2x1 +3x2 +2x+ x-5 17. Do the three lines xi - 4x2 In Exercises 7-10, the augmented matrix of a linear system has been reduced by row operations to the form shown. In each case continue the appropriate row operations and describe the solution set of the original system. x1-3x2-4 have a common Explain. 18. Do the three planes x + 2x2 +x Xi + 3x2 = 0 have at least one con tion? Explain 1 73 -4 0 1 -1 3 0 0 -2 1-1 00-41 1-4 9 0 8. 0 170 7. In Exercises 19-22, determine the value matrix is the augmented matrix of a consis
Web4 P Login zy zyBooks My lbrary WeBWorK : Math3... math examCouchtuner- Wat.. 4. Find the point of intersection of the lines x-5x: = 1 and Determine if the systems in Exercises 15 and i 6 are consistent Do not completely solve the systems 3x1-7x2 = 5. Consider each matrix in Exercises 5 and 6 as the augmented matrix of a linear system. State in words the next two elementary row operations that should be performed in the process of solving the system. 3x4=3 -2x2 + 3x3 + 2x4-1 14 5 07 01 -3 0 6 0 0 1 0 2 L0 001-5 1 -6 4 0 1 5. 16. X 2x2 2x 0 6. 0 0 1 2 3 -2x, +3x2 + 2x3 +x4 = 5 17. Do the three lines X1-4x2=1. 2n-x2--3. and In Exercises 7-10, the augmented matrix of a linear system has been reduced by row operations to the form shown. In each case, continue the appropriate row operations and describe the solution set of the original systerm -x-34 have a common point of intersection Explain. 18. Do the three planes x-+ 2x2 + x) = 4, x,-x3-1, and 1 7 3- 0 1 -1 3 XI +3x2 = 0 have at least one common point of inene tion? Explain. 8. 0 1 70 In Exercises 19-22, determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear sysiem. 0 0 1 -2 1 -1 0 0 1-3 0 0 1 -3 19. 20. -2 4 6 し0 0 0 2 21. 22.6 9 5 1 -2 03 2 0 1 0-47 In Exercises 23 and 24, key statements from this section ant either quoted directly, restated slightly (but still true), or allere in some way that makes them false in some cases. Mark each statement True or False, and justify your answer. (If true. give 0 0 01-3 Solve the systems in Exercises 11-14 ximate location where a similar statement appears, or to a definition or theorem. If false, give the location of a statcmen that has been quoted or used incorrectly, or cite an shows the statement is not true in all cases.) Similar true lalse questions will appear in many sections of the text. x2 + 4x3 =-5 3x1 +7x + 7x6 40 Du FS
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