txheem
Hauv kev tshaj tawm no, peb yuav txiav txim siab lub ntsiab lus ntawm qib ntawm matrix, nrog rau cov txheej txheem uas nws tuaj yeem pom. Peb kuj tseem yuav txheeb xyuas cov piv txwv los qhia txog kev siv txoj kev xav hauv kev xyaum.
Kev txiav txim siab qib ntawm matrix
Matrix qeb yog qhov qeb duas ntawm nws qhov system ntawm kab lossis kab. Txhua lub matrix muaj nws cov kab thiab kab ke, uas yog sib npaug rau ib leeg.
Kab system qeb yog qhov siab tshaj plaws ntawm cov kab uas tsis muaj kab. Qhov qeb duas ntawm kab ke yog txiav txim siab zoo ib yam.
Sau ntawv:
- Qhov qeb duas ntawm lub xoom matrix (nrog rau lub cim "θ") ntawm qhov loj me yog xoom.
- Qhov qeb duas ntawm ib qho nonzero kab vector lossis kab vector yog sib npaug rau ib qho.
- Yog hais tias ib tug matrix ntawm ib tug loj npaum li cas muaj tsawg kawg yog ib lub caij uas tsis sib npaug zos rau xoom, ces nws qib tsis tsawg tshaj li ib.
- Qhov qeb duas ntawm ib tug matrix tsis ntau tshaj nws qhov tsawg kawg nkaus dimension.
- Elementary transformations ua nyob rau hauv lub matrix tsis hloov nws qib.
Nrhiav qhov qeb duas ntawm lub matrix
Fringing Minor Method
Qhov qeb duas ntawm ib tug matrix yog sib npaug rau qhov siab tshaj plaws kev txiav txim ntawm ib tug nonzero .
Lub algorithm yog raws li nram no: nrhiav cov menyuam yaus los ntawm qhov kev txiav txim qis tshaj mus rau qhov siab tshaj. Yog me nqhov kev txiav txim tsis sib npaug rau xoom, thiab tag nrho cov tom ntej (n+1) yog sib npaug rau 0, yog li qib ntawm matrix yog n.
Piv txwv li
Yuav kom ua kom pom tseeb, cia peb ua ib qho piv txwv thiab nrhiav cov qib ntawm matrix A hauv qab no, siv txoj kev ciam teb cov menyuam yaus.
tshuaj
Peb tab tom cuam tshuam nrog 4 × 4 matrix, yog li ntawd, nws qib tsis tuaj yeem siab dua 4. Tsis tas li ntawd, muaj cov ntsiab lus tsis yog xoom hauv matrix, uas txhais tau tias nws qib tsis tsawg dua ib qho. Yog li cia peb pib:
1. Pib kuaj cov menyuam yaus ntawm qhov kev txiav txim thib ob. Yuav pib nrog, peb coj ob kab ntawm thawj thiab thib ob kab.
Minor sib npaug zero.
Yog li ntawd, peb tsiv mus rau tus me me tom ntej (thawj kem tseem nyob, thiab tsis yog qhov thib ob peb coj peb).
Cov menyuam yaus yog 54≠0, yog li qib ntawm matrix tsawg kawg yog ob.
Nco ntsoov: Yog tias qhov me me no tau muab sib npaug rau xoom, peb yuav txuas ntxiv xyuas cov kev sib txuas hauv qab no:
Yog tias xav tau, tus lej suav tuaj yeem txuas ntxiv mus rau tib txoj hauv kev nrog cov hlua:
- 1 thiab 3;
- 1 thiab 4;
- 2 thiab 3;
- 2 thiab 4;
- 3 thiab 4.
Yog tias txhua tus menyuam yaus thib ob tau sib npaug rau xoom, ces qib ntawm matrix yuav sib npaug rau ib qho.
2. Peb tswj yuav luag tam sim ntawd kom nrhiav tau tus menyuam yaus uas haum rau peb. Yog li cia peb txav mus rau cov menyuam yaus ntawm qhov kev txiav txim thib peb.
Rau qhov pom me me ntawm qhov kev txiav txim thib ob, uas tau muab qhov tshwm sim tsis yog xoom, peb ntxiv ib kab thiab ib qho ntawm cov kab uas tseem ceeb hauv ntsuab (peb pib ntawm qhov thib ob).
Cov menyuam yaus hloov mus ua xoom.
Yog li ntawd, peb hloov kab thib ob mus rau plaub. Thiab ntawm qhov kev sim thib ob, peb tswj kom pom tus me me uas tsis sib npaug ntawm xoom, uas txhais tau hais tias qib ntawm matrix tsis tuaj yeem tsawg dua 3.
Nco ntsoov: Yog hais tias qhov tshwm sim tau hloov mus rau xoom dua, es tsis txhob ntawm kab thib ob, peb yuav muab qhov thib plaub ntxiv thiab txuas ntxiv mus rau qhov "zoo" me.
3. Tam sim no nws tseem yuav txiav txim siab cov menyuam yaus ntawm qhov kev txiav txim plaub raws li qhov tau pom ua ntej. Nyob rau hauv cov ntaub ntawv no, nws yog ib tug uas phim lub determinant ntawm lub matrix.
Minor sib npaug 144≠0. Qhov no txhais tau hais tias qib ntawm matrix A sib 4.
Txo ntawm ib tug matrix mus rau ib tug stepped daim ntawv
Qhov qeb duas ntawm ib kauj ruam matrix yog sib npaug rau tus naj npawb ntawm nws cov kab uas tsis yog xoom. Ntawd yog, txhua yam peb yuav tsum tau ua yog coj cov matrix mus rau daim ntawv tsim nyog, piv txwv li, siv , uas, raws li peb tau hais los saum no, tsis txhob hloov nws qib.
Piv txwv li
Nrhiav qhov qeb duas ntawm lub matrix B hauv qab no. Peb tsis ua piv txwv ntau dhau, vim tias peb lub hom phiaj tseem ceeb tsuas yog ua kom pom kev siv cov qauv hauv kev xyaum.
tshuaj
1. Ua ntej, rho tawm thawj zaug ntawm kab thib ob.
2. Tam sim no rho thawj kab ntawm kab thib peb, muab faib ua plaub.
Yog li, peb tau txais ib kauj ruam matrix uas tus naj npawb ntawm cov kab uas tsis yog xoom yog sib npaug rau ob, yog li nws qib kuj sib npaug rau 2.