Numerical Solutions of Linear Systems of Equations

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EE 216 Class NotesD =2− 35− 45357− 8= −33636 − 4 5D1 = 7 5 7 = − 672− 31 3 − 82 36 5D2= − 3 7 7 = 10085 − 31 − 82 − 4 36D3 = − 3 5 7 = −13445 3 − 31x− 672− 33611= == DD2xx1008− 33622= = −= DD= DD− 1344=− 33633=43Pages 12 of 21
EE 216 Class NotesSolve the following set of linear equations.x 1 + x 2 + x 3 = 2 … … (1)2x 1 + 5x 2 + 3x 3 = 11 … … (2)- x 1 + 2x 2 + x 3 = 3 … … (3)Solution by Matrix InversionConsider the following set of linear equations.a =11x1+ a12x2+ a13x3b1a =21x1+ a22x2+ a23x3b2a =31x1+ a32x2+ a33x3b3… … (1)… … (2)… … (3)The system of equations above can be written in matrix form as:⎡aa⎢⎢⎢⎣a112131aaa122232aaa132333⎤ ⎡ xx⎥⎥⎥⎦ ⎢⎢⎢⎣x123⎤⎥⎥⎥⎦=⎡bb⎢⎢⎢⎣b123⎤⎥⎥⎥⎦[A][x] = [B]where[ A]=⎡aa⎢⎢⎢⎣a112131aaa122232aaa132333⎤⎥⎥⎥⎦Pages 13 of 21
Page 3: EE 216 Class NotesGAUSS ELIMINATION
Page 7 and 8: EE 216 Class NotesEqn. (1) (Row 1)
Page 11: EE 216 Class NoteswhereD =aaa112131
Page 15 and 16: EE 216 Class NotesBased on the abov
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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