(Solved): Consider the following traffic flow diagram, and use it to answer questions \\( 1,2,3,4 \\), and 5 ...

Consider the following traffic flow diagram, and use it to answer questions \\( 1,2,3,4 \\), and 5 . 1. Assume that the \\( i \\)-th column of the augmented matrix of the system of linear equations that describes this traffic flow diagram is associated with the variable \\( x_{i} \\). What is the line that represents the flow of traffic through intersection D? A) \\( \\left(\\begin{array}{llllll}0 & 0 & 0 & 1 & 0 & -1 \\mid 50\\end{array}\\right) \\), B) \\( \\left(\\begin{array}{llllll}0 & 0 & 0 & 1 & 0 & -1 \\mid 90\\end{array}\\right) \\) C) \\( (000-101 \\) 50) D) \\( \\left(\\begin{array}{llllll}0 & 0 & 0 & -1 & 0 & 1\\end{array} \\mid 130\\right) \\), E) None of the above 2. What is the minimum number of cars that can pass along \\( x_{4} \\) (between intersections \\( \\mathrm{B} \\) and D)? A) 40 B) 50 C) 130 D) 90 E) None of the above. 3. Assume that \\( x_{1}=10 \\) and \\( x_{4}=110 \\). Determine the number of cars that will be leaving the intersection D towards \\( \\mathrm{C} \\) (the value of \\( x_{6} \\) ). A) 30 B) 40 C) 50 D) 60 E) None of the above. 4. Would the system of linear equations describing the traffic flow diagram be square, overdetermined, underdetermined, or none of the above? A) Square B) Overdetermined C) Underdetermined D) None of the above. 5. How many free variables are in this system? A) at least 4 B) 0 C) at least 1 D) at least 3 E) None of the above.