A new shopping mall is built in town. This shopping mall has 5 gates, three of them only for entry (A, B, C) and the last two are exit only (D, E). This Christmas, you are interested in renting a small stand at this mall to sell your products. You talk to the mall administration and request the available stand locations. They give you the map below, and tell you that there's a free stand at every corridor (X1, X2 ... X7) X7 5 5 A E x6 X4 x1 X5 D B 2 x2 C x3 3 5 This map also shows you the average number of customers per minute that enter/exit each gate. For example, 2 customers per minute enter Gate B and 5 customers per minute exit from Gate D. a. (Op) Without calculating anything, just take a moment to review the map and make an educated guess to choose the best corridor to start your business. You obviously want more people traffic on the corridor you have your stand. You will not be graded for your answers here. I just want to create an opportunity for you to compare your intuition and the math. b. (10p) Since people won't disappear from existence at the gates of this mall (I hope), the number of people entering and exiting should be equal. Like we did in class for the traffic example, set the equations for each Gate of the map, as the first step. c. (10p) Using these equations form the Ax=b. d. (40p) Apply Gauss Jordan Elimination to obtain the reduced echelon form of the matrix A (don't forget the b while you are operating on A!) e. (30p) Find the free variables, particular solution for setting the free variables to zero. Based on the particular solution, which corridor is the most advantageous? Were you right in your first guess? f. (10p) Find the Null Space of A. What does this Null Space correspond to in your shopping mall?

A new shopping mall is built in town. This shopping mall has 5 gates, three of them only for entry (A, B, C) and the last two are exit only (D, E). This Christmas, you are interested in renting a small stand at this mall to sell your products. You talk to the mall administration and request the available stand locations. They give you the map below, and tell you that there's a free stand at every corridor (x1,x2x7) This map also shows you the average number of customers per minute that enter/exit each gate. For example, 2 customers per minute enter Gate B and 5 customers per minute exit from Gate D. a. (0p) Without calculating anything, just take a moment to review the map and make an educated guess to choose the best corridor to start your business. You obviously want more people traffic on the corridor you have your stand. You will not be graded for your answers here. 1 just want to create an opportunity for you to compare your intuition and the math. b. (10p) Since people won't disappear from existence at the gates of this mall (1 hope), the number of people entering and exiting should be equal. Like we did in class for the traffic example, set the equations for each Gate of the map, as the first step. c. (10p) Using these equations form the Ax=b. d. (40p) Apply Gauss Jordan Elimination to obtain the reduced echelon form of the matrix A (don't forget the b while you are operating on Al) e. (30p) Find the free variables, porticular solution for setting the free variables to zero. Based on the particular solution, which corridior is the most advantageous? Were you right in your first guess? f. (10p) Find the Null Space of A. What does this Null Space correspond to in your shopping mall? A new shopping mall is built in town. This shopping mall has 5 gates, three of them only for entry (A, B, C) and the last two are exit only (D, E). This Christmas, you are interested in renting a small stand at this mall to sell your products. You talk to the mall administration and request the available stand locations. They give you the map below, and tell you that there's a free stand at every corridor (x1,x2x7) This map also shows you the average number of customers per minute that enter/exit each gate. For example, 2 customers per minute enter Gate B and 5 customers per minute exit from Gate D. a. (0p) Without calculating anything, just take a moment to review the map and make an educated guess to choose the best corridor to start your business. You obviously want more people traffic on the corridor you have your stand. You will not be graded for your answers here. 1 just want to create an opportunity for you to compare your intuition and the math. b. (10p) Since people won't disappear from existence at the gates of this mall (1 hope), the number of people entering and exiting should be equal. Like we did in class for the traffic example, set the equations for each Gate of the map, as the first step. c. (10p) Using these equations form the Ax=b. d. (40p) Apply Gauss Jordan Elimination to obtain the reduced echelon form of the matrix A (don't forget the b while you are operating on Al) e. (30p) Find the free variables, porticular solution for setting the free variables to zero. Based on the particular solution, which corridior is the most advantageous? Were you right in your first guess? f. (10p) Find the Null Space of A. What does this Null Space correspond to in your shopping mall