Ryan Ren Math4A-02-S17-Williams WeBWorK assignment number Week1 is due : 04/10/2017 at 06:01am PDT. The Gauchospace link for the course contains the syllabus, grading policy and other information. The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are having trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA's or your professor for help. Don't spend a lot of time guessing - it's not very efficient or effective. Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2 3 instead of 8, sin(3 pi/2)instead of -1, e (ln(2)) instead of 2, (2 + tan(3)) (4 sin(5)) 6 7/8 instead of 27620.3413, etc. Here's the list of the functions which WeBWorK understands. You can use the Feedback button on each problem page to send e-mail to the professors. What is the augmented matrix of the sytem? 1. (1 pt) Use elementary row operations to find the reduced row echelon form of 8 0 0 8 16 24 11 8 12 0 24 36 Find the reduced row echelon form of this augmented matrix. ? 1. What is the nature of the solution(s) of the system? !- Answer(s) submitted: Which columns are pivot columns? Enter the sum of the column numbers. For instance if the first and third columns were pivot columns then your answer would be 1+3=4. !Answer(s) submitted: (incorrect) 2. (1 pt) Consider the system x y 2z = 15 2x + 3y + z = 15 5x + 4y + 2z = 5 (incorrect) 3. (1 pt) 1 Consider the system 3x1 + 3x2 + 6x3 = 0 2x1 x2 + x3 = 0 14x1 4x2 + 10x3 = 0 What is the augmented matrix of the sytem? !Answer(s) submitted: (incorrect) Find the reduced row echelon form of this augmented matrix. 5. (1 pt) 1 3 9 Consider the matrix 0 0 0 0 0 0 Which condition or conditions of being in RREF does the matrix fail? ? 1. What is the nature of the solution(s) of the system? !- A. Zero rows are at the bottom B. The leftmost nonzero entry of each nonzero row equals 1 C. Each pivot is further to the right than the pivot in the row above it D. Each pivot is the only nonzero entry in its column E. None of the above, it is in RREF Answer(s) submitted: !Answer(s) submitted: (incorrect) 6. (1 pt) 1 6 4 3 0 1 2 4 Consider the matrix 0 0 0 1 0 0 0 0 Which condition or conditions of being in RREF does the matrix fail? A. Zero rows are at the bottom B. The leftmost nonzero entry of each nonzero row equals 1 C. Each pivot is further to the right than the pivot in the row above it D. Each pivot is the only nonzero entry in its column E. None of the above, it is in RREF (incorrect) 4. (1 pt) !- Answer(s) submitted: of k which make the augmented matrix \u0014 Determine any values \u0015 1 2 10 -9 inconsistent. 3 4 -7 k Enter your answers in increasing order. If less than 3 values of k make it inconsistent, enter X into any blanks you wouldn't use. If all values of k make it inconsistent enter A into all 3 blanks. (incorrect) 7. (1 pt) 1 Consider the matrix 0 0 2 7 0 0 0 1 0 5 2 0 0 0 1 Which condition or conditions of being in RREF does the matrix fail? A. Zero rows are at the bottom B. The leftmost nonzero entry of each nonzero row equals 1 C. Each pivot is further to the right than the pivot in the row above it D. Each pivot is the only nonzero entry in its column E. None of the above, it is in RREF !- (incorrect) 10. (1 pt) Solve the system using matrices (row operations) \u001a x= y= Answer(s) submitted: Answer(s) submitted: (incorrect) (incorrect) 8. (1 pt) 12. (1 pt) Solve the system using matrices (row operations) Use elementary row operations to find the reduced row echelon form of 1 3 8 0 2 7 18 1 0 1 2 4 2x+3y=23 9x8y= 90 4x4y5z=1 5x+6y4z= 1 6x5y+2z=4 x= y= z= Answer(s) submitted: Which columns are pivot columns? Enter the sum of the column numbers. For instance if the first and third columns were pivot columns then your answer would be 1+3=4. (incorrect) !Answer(s) submitted: 13. (1 pt) Write the augmented matrix of the system +6z= 8 48x 9x +2y z=1 33x+42y =2 Answer(s) submitted: (incorrect) 9. (1 pt) Solve the system using substitution \u001a x 4y=3 3x11y=1 x= y= Answer(s) submitted: (incorrect) 3 19. (1 pt) Solve the system \u001a x1 +x2 +4x3 =9 3x1 +4x2 +3x3 =1 x1 + s. x2 = x3 14. (1 pt) Determine the value of h such that the matrix is the augmented matrix of a consistent linear system. \u0014 \u0015 8 6 h 16 12 2 h= Answer(s) submitted: Answer(s) submitted: (incorrect) (incorrect) 20. (1 pt) Solve the system x1 x2 3x3 = 6 5x1 4x2 7x3 = 9 3x1 15x3 =45 x1 + s. x2 = x3 15. (1 pt) Determine the value of h such that the matrix is the augmented matrix of a linear system with infinitely many solutions. \u0014 \u0015 4 8 3 16 h 12 h= Answer(s) submitted: Answer(s) submitted: (incorrect) (incorrect) 21. (1 pt) Solve the system x1 +4x3 +2x4 = 13 x2 2x3 4x4 = 11 3x1 3x2 +19x3 +18x4 = 13 x2 +2x3 +9x4 =36 x1 = x2 = x3 = x4 = 16. (1 pt) Solve the equation x y = z 4x + 9y + 9z = 1. + s + t. Answer(s) submitted: (incorrect) 17. (1 pt) Determine the value of k for which the system x +y+5z=3 x+2y2z=3 2x+8y+kz=7 Answer(s) submitted: has no solutions. k= (incorrect) Answer(s) submitted: (incorrect) 18. (1 pt) Solve the system \u001a 2x1 +x2 = 7 4x1 +2x2 =14 \u0015 \u0014 \u0015 \u0014 \u0015 \u0014 x1 + s. = x2 Answer(s) submitted: 22. (1 pt) Solve the system x1 +x2 = 2 x2 +x3 =1 x +x =2 3 4 x1 +x4 = 1 x1 x2 + s. = x3 x4 Answer(s) submitted: (incorrect) (incorrect) 4 x1 x2 x3 = x4 23. (1 pt) Solve the system 5x1 4x2 +4x3 +3x4 = 1 x1 +x2 +3x3 +3x4 = 5 4x1 3x2 +7x3 +6x4 = 6 2x1 +2x2 +6x3 +6x4 =10 + Answer(s) submitted: (incorrect) c Generated by WeBWorK, http://webwork.maa.org, Mathematical Association of America 5 s + t