Problem 9. (1 point) A dietitian is planning a meal that supplies certain quantities of vi- tamin C, calcium, and magnesium. Three foods containing these nutrients will be used. The amount of each nutrient, in milligrams, found in one unit of each food is given in the table below, along with the dietary requirements. Nutrient | Food 1 | Food 2 | Food 3 | Total Required (mg) Vitamin C 50 50 50 375 Calcium 40 60 60 390 Magnesium 30 50 40 290 (a) Write the augmented matrix for this problem: (b) What quantity of Food 1 is necessary to meet the dietary re- quirements? Answer: units (c) What quantity of Food 2 is necessary to meet the dietary re- quirements? Answer: units (d) What quantity of Food 3 is necessary to meet the dietary re- quirements? Answer: units Answer(s) submitted: (incorrect) Problem 10. (1 point) The reduced row echelon form of a system of linear equations in x and y or in x, y and z is given. For each system, determine whether it has a unique solution, infinitely many solutions, or no solutions. (@) 1 0 0| 3 01 0] 3 00 0] O e A. Unique solution: x=0,y=0,z=0 e B. No solutions e C. Unique solution: x =3,y =3 e D. Unique solution:x =3,y =3 o E. Infinitely many solutions e F None of the above (b) (@) 1 0 00 010 110 0 A. Infinitely many solutions B. Unique solution: x =0,y =0,z=0 C. Unique solution: x =1,y =1,z=0 D. No solutions E. Unique solution: x=0,y =0 E. None of the above 1 00 010 0 00 A. No solutions 4 4 -3 B. Unique solution: x = 4,y = 4 C. Unique solution: x = 4,y =4,z=0 D. Unique solution: x = 4,y = 4,z= -3 E. Infinitely many solutions F. None of the above A. Unique solution: B. Unique solution: C. No solutions 0| 0 0| 4 | -2 =0,y=4,z=-2 = 747y: 72 D. Unique solution: x =0,y = 4 o E. Infinitely many solutions o F. None of the above Answer(s) submitted: (incorrect) Problem 11. (1 point) 4 2 4 3 3 3 LetA=| 0 4 -1 |andB=| -1 -2 1 1 4 3 -1 0 -2 Determine 4A B. Answer(s) submitted: (incorrect) Problem 12. (1 point) Determine the following product. -5 [4 =2 3 5] :}1 = 4 [] Answer(s) submitted: (incorrect) Problem 13. (1 point) Problem 14. (1 point) Consider the matrices Let A = 3 ; James-[ & L - W Perform the indicated operations. Of the possible matrix products ABC, ACB, BAC, BCA, CAB, CBA, (a) AB = 1 1 which make sense? 1 1 Note: Enter A for A. (i.e. don't include the '.'), etc. in the (b) BA = pace provided (options given below). Answer(s) submitted: Answer: . A. ( ACB, BAC, CBA ) only B. ( ABC, BCA, CAB ) only . C. ( ACB, BAC, CAB ) only D. all of them . E. none of them submitted. (incorrect) . . . (incorrect)Problem 15. (1 point) The matrix on the right results after performing a single row op- eration on the matrix on the left. -1 4 4 1 32 8 3 -5 4 -1 0 | rowop produces: | 5 4 1 0 -2 1 -2 -1 -2 1 -2 -1 Identify the row operation. Use R1, R2, and R3 to represent the rows Ry, Ry, and R3. For example, if the operation were \"add 2 times row 4 to row 6\" then the answer would be 72 % R4 +R6 R6\". If it were \"swap row 4 with row 6\" the answer would be \"R4 /] Answer(s) submitted: (incorrect) Problem 16. (1 point) Given the augmented matrix 1 3 3| 6 A= 4 13 -6 1], -2 -9 5|-=2 perform each row operation in the order specified and enter the final result. First: R) 4Ry Ry, Second: R3 +2R; R3, Third: R3 + 3Ry R3. Answer(s) submitted: (incorrect) Problem 17. (1 point) For the following system to be consistent, 3x 6y5z=4 15x54y+kz =15 6x 9y+3z= 7 we must have, k # Answer(s) submitted: (incorrect) Problem 18. (1 point) Linear System - Three Variables 1000 0 0110 -l Led= 5 68 1 3 0000 0 Is the matrix in row echelon form? (input Yes or No) If this matrix were the augmented matrix for a system of linear equations, would the system have no, unique, or many solutions (input no or unique or many)? Answer(s) submitted: o (incorrect) Problem 19. (1 point) Problem 20. (1 point) Sally went to the store and purchased 4 skirts, 3 dresses and 3 During the month of January, "ABC Appliances" sold 54 mi- shirts. Anna went to the store and purchased 4 skirts, 3 dresses crowaves, 21 refrigerators and 49 stoves, while "XYZ Appli- and 5 shirts. ances" sold 52 microwaves, 17 refrigerators and 42 stoves. Each skirt costs $12, each dress cost $23, and each shirt costs $12. During the month of February, "ABC Appliances" sold 28 mi- a) Write a 2 x 3 matrix summarizing the purchases made by Sally crowaves, 34 refrigerators and 28 stoves, while "XYZ Appli- and Anna. (Keep the order of information) ances" sold 47 microwaves, 15 refrigerators and 17 stoves. a) Write a 2 x 3 matrix summarizing the sales for the month of January. (Keep the order of information). b) Write a 3 x 1 matrix summarizing the cost (in dollars) of the items. (Keep the order of information) b) Write a 2 x 3 matrix summarizing the sales for the month of February. (Keep the order of information). c) Use matrix multiplication to find a 2 x 1 matrix summarizing the total amount (in dollars) spent by Sally and Anna. c) Use matrix addition to find a 2 x 3 matrix summarizing the total sales for the months of January and February Answer(s) submitted: Answer(s) submitted: . . (incorrect) . . (incorrect) Generated by OWeBWork, http://webwork. maa.org, Mathematical Association of America