Lub inverse matrix los yog invertible matrix yog ib hom ntawm square txhoj, uas yog, nws muaj tib cov kab (m) thiab txhua (n).

Nws tshwm sim thaum cov khoom ntawm ob qho kev pom zoo ua rau a qhia txog tus kheej matrix ntawm tib qho kev txiav txim (tib cov kab thiab kab ntawv).

Yog li no, txhawm rau txhawm rau paub qhov tsis hloov ntawm ib tus lej ntawm lej, txhooj yog siv.

A. B = B. A = Kuvn (thaum matrix B tsis rov qab txog ntawm Matrix A)

Tab sis dab tsi yog qhov cim npe hauv keeb kwm?

Daim duab qhia txog tus kheej yog txhais thaum lub ntsiab ntawm cov kab pheeb ces kaum txhua yam sib npaug ntawm 1 thiab lwm qhov sib npaug yog sib npaug 0 Nws yog qhia los ntawm kuvn:

Inverse matrix thaj chaw

  • Tsuas muaj ib qho rov qab rau txhua tus matrix
  • Tsis yog txhua zaus yuav tsum muaj qhov sib hloov pauv. Nws yog invertible tsuas yog thaum cov khoom lag luam ntawm cov square matrices tshwm sim nyob rau hauv ib qho keeb ntawm keeb (Kuvn)
  • Txoj kev ntsuas qhov tsis hloov ntawm ib qho kev rov hloov dua siab sib raug ntawm tus lej nws tus kheej: A = (A-1)-1
  • Lub transpose kev tsim ntawm ib qho kev rov tsis sib hloov kuj yog ua rov qab: (At) -1 = (AW-1)t
  • Qhov rov ua sab nraud ntawm ib qho transpose matrix ua rau qhov hloov pauv hloov siab: (A-1 Unt) -1
  • Txoj kev ntsuas qhov hloov pauv ntawm ib tus kheej cov lus sib npaug yog tib yam li cov cim kev ua lag luam: I-1 = Kuv

kuj pom thiab: Arrays

Piv txwv inverse matrix

2 × 2 rov qab sib npaug

3 × 3 rov qab sib npaug

Ib kauj ruam zuj zus: yuav ua li cas los laij cov inverse matrix?

Peb paub tias yog cov khoom lag luam ntawm ob qho kev ua lag luam sib npaug sib luag ntawm tus kheej matrix, qhov matrix muaj qhov rov ua.

Nco ntsoov tias yog tias matrix A tsis rov qab ntawm Matrix B, cov cim sau cia: A-1.

Piv txwv: Nrhiav qhov sib xyaw kom haum ntawm hauv matrix hauv qhov kev txiav txim 3 × 3.

Ua ntej tshaj plaws, peb yuav tsum nco ntsoov qhov ntawd. A-1 = Kuv (Tus lej loj uas khoo cov los ntawm nws rov qab los yuav ua rau yog leej twg lub matrix)n)

Txhua ntu hauv thawj kab ntawm thawj ntu kev sib npaug yog khoo txhua kab lus ntawm kab ntawv thib ob.

Yog li no, cov ntsiab ntawm kab thib ob ntawm thawj qhov kev sib npaug yog khoo khoo los ntawm cov lej ntawm ob.

Thiab thaum kawg, kab thib peb ntawm thawj daim ntawv nrog kab ntawm tus thib ob:

Los ntawm kev sib luag ntawm cov khoom nrog cov cim ntawm tus kheej, peb tuaj yeem tshawb pom qhov tseem ceeb ntawm:

ua = 1
b = 0 hli
c = 0 hli

inverse matrix thaj chaw

Paub txog cov txiaj ntsig no, peb tuaj yeem suav lwm qhov tsis paub hauv ntu. Hauv kab thib peb thiab thawj kem ntawm thawj kab ntawv peb muaj + 2d = 0. Yog li, cia peb pib los ntawm kev pom cov nqi ntawm d, los ntawm kev hloov tus nqi pom:

1 + 2d = 0
2d = -1
d = -1/2 -np

Zoo sib xws, hauv kab thib peb thiab kab thib ob peb tuaj yeem nrhiav tus nqi ntawm y:

b + 2e = 0
0 + 2e = 0
2e = 0 ib
e = 0/2
e: 0 ua

Tsiv mus rau hauv, peb muaj nyob rau hauv kab hauv qab kawg ntawm peb sab: c + 2f. Nco ntsoov tias, thib ob, cov cim kev ua lag luam ntawm qhov sib npaug no tsis yog xoom, tab sis sib npaug rau 1.

c + 2f = 1
0 + 2f = 1
2f = 1 ib
f = ½ cov

Mus rau kab thib ob thiab kab thib ib, peb yuav pom tus nqi ntawm g:

ib + 3d + g = 0
1 + 3. (-1/2) + g = 0
1 - 3/2 + g = 0
g = -1 + 3/2
g = ½ ib

Hauv kab ob thiab kem ob, peb tuaj yeem nrhiav tus nqi h:

b + 3e + h = 1
0 + 3 + h = 0
h = 1 os

Thaum kawg, cia peb pom lub txiaj ntsig yo los ntawm kab zauv ntawm kab thib ob thiab kab ntawv thib peb:

c + 3f + kuv = 0
0 + 3 (1/2) + kuv = 0
3/2 + kuv = 0
kuv = 3/2

 

Vestibular ce nrog cov tswv yim

1Cov. (Cefet-MG) Kev nteg ntoo tsis sib luag
Nws tuaj yeem hais qhov tseeb tias qhov sib txawv (xy) sib npaug:

ib) -8
b) -2
c) 2
d) 6
e) 8 hli

2Cov. (UF Viçosa-MG) Cov lus hauv qab no yog:

Qhov x thiab y yog tus lej tiag thiab M yog kev ntsuas hloov ntawm A. Yog li ntawd, cov khoom xy yog:

a) 3/2 ib
b) 2/3
c) 1/2 ib
d) 3/4 ib
e) 1/4

3Cov. (PUC-MG) Kev ntsuas qhov tsis ncaj ntawm cov ntawv sib npaug yog sib npaug:

a)
b)
c)
d)
e)