eview Opersi Mtriks Menghitung invers mtriks? Determinn? Mtriks Singulr?
Menghitung invers mtriks
Determinn Hny untuk squre mtries b d d b d b det Jik determinn mtriks singulr, tidk puny invers det b b b b b b b b b
Cri invers ny
Sistem Persmn Liner Simultneous Liner Equtions
Metode Penyelesin Metode grfik Eliminsi Guss Metode Guss Jourdn Metode Guss Seidel LU deomposition
Metode Grfik Det{A} A is nonsingulr so invertible Unique solution -
Sistem persmn yng tk terselesikn No solution Det [A], but system is inonsistent Then this system of equtions is not solvble
Sistem dengn solusi tk terbts Det{A} A is singulr infinite number of solutions 8 Consistent so solvble
Ill-onditioned system of equtions A liner system of equtions is sid to be illonditioned if the oeffiient mtri tends to be singulr
Ill-onditioned system of equtions A smll devition in the entries of A mtri, uses lrge devition in the solution...99.8..99.9
Gussin Elimintion Merupkn slh stu teknik pling populer dlm menyelesikn sistem persmn liner dlm bentuk: [ A ][ X] [ C] Terdiri dri du step. Forwrd Elimintion of Unknowns.. Bk Substitution
Forwrd Elimintion Tujun Forwrd Elimintion dlh untuk membentuk mtriks koefisien menjdi Upper Tringulr Mtri 8.8..
Forwrd Elimintion Persmn liner n persmn dengn n vribel yng tk dikethui... n n b n n... b... n n...... n nn n b n
Contoh 8 mtriks input 8 8
Forwrd Elimintion 8 9 9 9 9 9 9 9 9 9
Forwrd Elimintion 9 9 9 9 9 9 9 9 9 9
Bk substitution 9 9
Guss - Jourdn 9 8 8
Wrning.. Du kemungkinn keslhn -Pembgin dengn nol mungkin terjdi pd lngkh forwrd elimintion. Mislkn:.99.9 - Kemungkinn error kren round-off (keslhn pembultn)
Contoh Dri sistem persmn liner.99.9.9.99 Akhir dri Forwrd Elimintion....
Keslhn yng mungkin terjdi Bk Substitution.....9999..
Contoh keslhn Bndung-kn solusi et dengn hsil perhitungn [ ] X [ ].9999.. X lulted [ ] X et
Improvements Menmbh jumlh ngk penting Mengurngi round-off error (keslhn pembultn) Tidk menghindrkn pembgin dengn nol Gussin Elimintion with Prtil Pivoting Menghindrkn pembgin dengn nol Mengurngi round-off error
Pivoting Eliminsi Guss dengn prtil pivoting mengubh tt urutn bris untuk bis mengpliksikn Eliminsi Guss ser Norml How? Di wl sebelum lngkh ke-k pd forwrd elimintion, temukn ngk mksimum dri: kk, k, k,......, nk Jik nili mksimumny Pd bris ke p, pk k p n, Mk tukr bris p dn k.
Prtil Pivoting Wht does it Men? Gussin Elimintion with Prtil Pivoting ensures tht eh step of Forwrd Elimintion is performed with the pivoting element kk hving the lrgest bsolute vlue. Jdi, Kit mengeek pd setip lngkh pkh ngk pling ts (pivoting element) dlh sellu pling besr
Prtil Pivoting: Emple Consider the system of equtions.9.99 In mtri form.99.9 Solve using Gussin Elimintion with Prtil Pivoting using five signifint digits with hopping
Prtil Pivoting: Emple Forwrd Elimintion: Step Emining the vlues of the first olumn, -, nd or,, nd The lrgest bsolute vlue is, whih mens, to follow the rules of Prtil Pivoting, we don t need to swith the rows.9.99.... Performing Forwrd Elimintion
Prtil Pivoting: Emple Forwrd Elimintion: Step Emining the vlues of the first olumn -. nd. or. nd. The lrgest bsolute vlue is., so row is swithed with row........ Performing the row swp
Prtil Pivoting: Emple Forwrd Elimintion: Step Performing the Forwrd Elimintion results in:....
Prtil Pivoting: Emple Bk Substitution Solving the equtions through bk substitution........
Prtil Pivoting: Emple Compre the lulted nd et solution The ft tht they re equl is oinidene, but it does illustrte the dvntge of Prtil Pivoting [ ] X et [ ] X lulted
Summry -Forwrd Elimintion -Bk Substitution -Pitflls -Improvements -Prtil Pivoting