Question

Matrix Algebra

Consider the traffic flow diagram that follows, where a1, az, a3, 24, 61, 62, 63, 64 are fixed positive integers. Set up a linear system in the unknowns X1, X2, X3, X4 and show that the system will be consistent if and only if a1 + a2 + a3 + 24 = 61 + b2 + b3 + 64 What can you conclude about the number of automobiles entering and leaving the traffic network? ai ba bi X1 04 X2 X4 02 X3 b3 b2 d3

Answer 1

ANSWER:
0 Here a treat foc flow deegram és geven where Q11 Q2, Qg? Qy' bis 62163, by aree fened pole teve enten geres . We are to set up a linear systery in the Unknown ni inanzisy and show that the systemy wou be conceptent of 'ond only of. atas taztay a bit bat batby conclude about the number of are to yobeles en entering and leaving the sework. what can we Also tratfche by ni ay bi ny bz 16 we dreaw the above traffic For ouere convenience flow diagrain as shown bllow-

au A 나 A by 103 Meest be Same as At each intersection the nelbere of automobiles entering the number leaving For example, at the entersection A, the number of automobiles enterings is ntau and the number leaving is x2 tbi 'Thus.. x + = Kathi Cinteresection A) seny el arely, instais Nz tbi (Intersection Azt az = xy tb3 (Intere section e) ay tay skit by . (Intere seete on D) Now, (U. non = berca nga bara2 xs-ny - bzraz -B) (W ney - mi by-ay