Numerical Solutions of Linear Systems of Equations

EE 216 Class NotesIt should be noted that Eqns. (3.1) – (3.3) have been derived based on the principle ofconservation of mass. Eqns. (3.4) and (3.5) have been derived based on the principle ofpressure drop along pipe sections.The set of equations can be solved by substitution method in the following manner.[A][Q] = [B]where[ A ]=⎡ 10129.9⎢⎢⎢⎢⎢⎢⎣ 01− 10− 29.90011− 3.93.90100− 7.90⎤0− 1019.9⎥⎥⎥⎥⎥⎥⎦⎡QQQ⎢⎢⎢⎢⎢⎢⎣QABAC⎤⎥⎥⎥⎥⎥⎥⎦[ Q] = Q and [ B]CBCDBD[ Q]= [A]−1 [ B]⎡0.03⎤0.06= 00⎢⎢⎢⎢⎢⎢⎣ 0⎥⎥⎥⎥⎥⎥⎦Pages 19 of 21