System of linear algebraic equations

Hauv kev tshaj tawm no, peb yuav txiav txim siab lub ntsiab lus ntawm cov kab ke ntawm kab zauv sib npaug (SLAE), nws zoo li cas, hom twg muaj, thiab tseem yuav qhia nws li cas hauv daim ntawv matrix, suav nrog qhov txuas ntxiv.

Cov ntsiab lus

Kev txhais ntawm ib qho system ntawm linear equations

System of linear algebraic equations (los yog "SLAU" luv luv) yog ib qho system uas feem ntau zoo li no:

System of linear algebraic equations

  • m yog tus lej ntawm qhov sib npaug;
  • n yog tus naj npawb ntawm cov hloov pauv.
  • x1,x2,..., xn - tsis paub;
  • a11,12…, amn - coefficients rau tsis paub;
  • b1b2, ..., ibm - cov tswv cuab dawb.

Coefficient Indices (aij) raug tsim raws li hauv qab no:

  • i yog tus naj npawb ntawm cov kab zauv sib npaug;
  • j yog tus naj npawb ntawm qhov sib txawv uas tus coefficient hais txog.

SLAU solution – cov lej ntawd c1, C2, ..., cn , nyob rau hauv qhov chaw uas tsis yog x1,x2,..., xn, txhua qhov sib npaug ntawm qhov system yuav tig mus rau hauv tus kheej.

Hom SLAU

  1. Homogeneous - tag nrho cov tswv cuab dawb ntawm qhov system sib npaug rau xoom (b1 =b2 = … = bm = 0).

    System of linear algebraic equations

  2. Heterogeneous - yog tias tsis tau raws li qhov xwm txheej saum toj no.
  3. square - tus lej ntawm qhov sib npaug yog sib npaug rau cov lej tsis paub, piv txwv li m = n.

    System of linear algebraic equations

  4. Tsis muaj kev txiav txim siab - tus naj npawb ntawm cov tsis paub yog ntau dua li cov lej sib npaug.

    System of linear algebraic equations

  5. kev hla dhau Muaj ntau qhov sib npaug tshaj qhov sib txawv.

    System of linear algebraic equations

Nyob ntawm tus naj npawb ntawm cov kev daws teeb meem, SLAE tuaj yeem yog:

  1. Joint muaj tsawg kawg yog ib qho kev daws teeb meem. Ntxiv mus, yog tias nws yog qhov tshwj xeeb, qhov system hu ua qhov tseeb, yog tias muaj ntau qhov kev daws teeb meem, nws yog hu ua indefinite.

    System of linear algebraic equations

    SLAE saum toj no yog sib koom ua ke, vim tias muaj tsawg kawg yog ib qho kev daws teeb meem: x = 2 os,y = 3.

  2. tsis sib xws Lub system tsis muaj kev daws teeb meem.

    System of linear algebraic equations

    Sab xis ntawm qhov sib npaug yog tib yam, tab sis sab laug tsis yog. Yog li, tsis muaj kev daws teeb meem.

Matrix cim ntawm qhov system

SLAE tuaj yeem sawv cev rau hauv daim ntawv matrix:

AX = B

  • A yog lub matrix tsim los ntawm cov coefficients ntawm cov tsis paub:

    System of linear algebraic equations

  • X - kab ntawm cov variables:

    System of linear algebraic equations

  • B - kem ntawm cov tswv cuab dawb:

    System of linear algebraic equations

Piv txwv li

Peb sawv cev rau qhov system ntawm kev sib npaug hauv qab no hauv daim ntawv matrix:

System of linear algebraic equations

Siv cov ntaub ntawv saum toj no, peb sau lub ntsiab matrix nrog coefficients, kab nrog cov neeg tsis paub thiab dawb.

System of linear algebraic equations

System of linear algebraic equations

System of linear algebraic equations

Ua kom tiav cov ntaub ntawv ntawm qhov muab qhov system ntawm qhov sib npaug hauv daim ntawv matrix:

System of linear algebraic equations

Extended SLAE Matrix

Yog hais tias mus rau lub matrix ntawm lub system A ntxiv cov tswvcuab dawb kab rau sab xis B, cais cov ntaub ntawv nrog ib tug ntsug bar, koj tau txais ib tug ncua matrix ntawm SLAE.

Rau qhov piv txwv saum toj no, nws zoo li no:

System of linear algebraic equations

System of linear algebraic equations- lub npe ntawm qhov txuas ntxiv matrix.

Sau ntawv cia Ncua