Numerical Solutions of Linear Systems of Equations

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EE 216 Class Notes⎡ x⎢⎢⎢⎣x1⎤⎥⎥⎥⎦[ x] = x and [ B]23=⎡bb⎢⎢⎢⎣b123⎤⎥⎥⎥⎦If D ≠ 0 , then the system has a unique solution.[x] = [A] -1 [B]A Traffic Light AssemblyzCDA6 m4 mhB3 mx4 m3 m4 m6 m4 m3 myFigure 1.1 A traffic light assemblyThe mass of the traffic light assembly is 20 kg and h = 3.5 m. For equilibrium,the forces acting on the light assembly in all three directions (x, y and z) should equal tozero.∑ x∑ y∑ zF = 0 , F = 0 and F = 0Pages 14 of 21
EE 216 Class NotesBased on the above, a set of equations in terms of the three unknown forces canbe written as:0 .5970F− 0.8381F+ 0.7960F= 0AB0 .7960F− 0.4191F− 0.5970F= 0AB0 .0995F0.3492F+ 0.0995F= 196.2ACACAB+ACADADAD… … (1)… … (2)… … (3)[A][F] = [B]where[ A ]⎡0.5970= 0.7960⎢⎢⎢⎣0.0995− 0.8381− 0.41910.34920.7960⎤− 0.59700.0995⎥⎥⎥⎦⎡F⎢⎢⎢⎣FAB⎤⎥⎥⎥⎦[ F ] = F and [ B]ACAD[ F ] = [A]−1 [ B]=⎡ 0⎤0⎢⎢⎢⎣196.2⎥⎥⎥⎦[ ]−A 1=⎡−⎢⎢⎢⎣0.35470.29480.67990.7685− 0.0421− 0.62071.7737⎤2.10560.8867⎥⎥⎥⎦[ F ]=⎡−⎢⎢⎢⎣0.35470.29480.67990.7685− 0.0421− 0.62071.7737⎤⎡ 0⎤2.1056 00.8867⎥⎥⎥⎦ ⎢⎢⎢⎣196.2⎥⎥⎥⎦Pages 15 of 21
Page 3: EE 216 Class NotesGAUSS ELIMINATION
Page 7 and 8: EE 216 Class NotesEqn. (1) (Row 1)
Page 11 and 12: EE 216 Class NoteswhereD =aaa112131
Page 13: EE 216 Class NotesSolve the followi
Page 17 and 18: EE 216 Class Notes[A][C] = [B]where
Page 19 and 20: EE 216 Class NotesIt should be note
Page 21: EE 216 Class NotesSolve the followi

Numerical Solutions of Linear Systems of Equations

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