Ileta yo y j misela izinto ezikhoyo kwimiqolo nakwiikholamu ngokwahlukeneyo.

A = (aij)MXN

Umzekelo: A3 × 3 (Imatriki A inemiqolo emithathu neekholamu ezintathu)

QaphelaKubalulekile ukuba uqaphele ukuba ekuphindaphindeni kwematriki, ukulandelelana kwezinto kuthintela umphumo wokugqibela. Oko kukuthi, ayitshintshi:

A. B ≠ B. A

## Ukubala: indlela yokuphindaphinda imatriki?

Vumela imatriki A = (aij)MXN kunye B = (bjk)nxp

A. B = matrix D = (dik)mxp

apho

dik = ai1 . b1k + ai2 . b2k +… + Aen . bnk

Ukubala imveliso phakathi kweematriki, kuya kufuneka sithathele ingqalelo imigaqo ethile:

Ukubala imveliso phakathi kweematriki ezimbini, kubalulekile ukuba n ilingane ne p (n = iphe)

Oko kukuthi, inani leekholamu kwimatriki yokuqala (n) kufuneka ilingane nenani lemigca (p) Kwimatriki yesibini.

Iziphumo eziveliswayo phakathi kwematriki ziya kuba zezi: ABmxp. (inani lemiqolo kwi matrix A Inani lamaxesha ekholamu kwimatriki B).

bona kwakhona: Ukufika

## Umzekelo wokuphindaphinda kweMatrix

Kulo mzekelo ulandelayo, sinayo i-matrix A yohlobo lwe-2 × 3 kunye ne-matrix B yohlobo lwe-3 × 2. Ke ngoko, imveliso phakathi kwabo (matrix C) iya kuba nesiphumo se-2 × 2 matrix.

Ekuqaleni, siya kuphinda-phinda izinto ze umgca 1 ka-A kunye nezo ikholamu 1 ka-B. Nje ukuba iimveliso zifunyenwe, masongeze onke la maxabiso:

2) 1 + 3. 0 + 1. 4 = 6

Ke ngoko, siza kuphinda-phinda kwaye songeze izinto ze umgca 1 ka-A kunye ikholamu 2 ka-B:

2) (-2) + 3. 5 + 1. 1 = 12

Emva koko, masiqhubeke umgca 2 ka-A kwaye phinda-phinda kwaye ungeze nge ikholamu 1 ka-B:

(-Nye). 1 + 1. 0 + 0. 2 = 4

Kusekho umgca 2 ka-A, siya kwanda kwaye songeze nge ikholamu 2 ka-B:

(-Nye). (-1) + 2. 0 + 5. 2 = 1

Okokugqibela, kufuneka siphindaphinde A. A. ngu:

## Phinda inani lokwenyani nge-matrix

Kwimeko yokuphindaphinda inani lokwenyani nge-matrix, kuya kufuneka uphindaphinda into nganye ye-matrix ngenani elo:

## Imatriki eguqulweyo

I matrix eguqulweyo luhlobo lwe matrix olusebenzisa ipropathi yokuphindaphinda:

A. B = B. A = Ngaphakathi (xa imatriki B iguqukile kwimatriki A)

Qaphela ukuba i-matrix eguqulweyo ka-A imelwe ngu-A-1.

## Ukuzivocavoca umzimba ngeempendulo

1. (PUC-RS) Umsebenzi

kunye no-C = A. B, isiqalelo C33 weMatrix C yile:

a) Ngama-9
b) 0
c) -4
d) -8
c) -12

2. (UF-AM) Yiba

kunye ne-AX = 2B. Ke matrix X ilingana no:

a)

b)

c)

d)

e)

3. (PUC-MG) Qwalasela uluhlu lwangempela lwezinto

Ukwazi oko. B = C, kunokuthiwa isixa sezinto ze Un :

a) Ngama-10
b) 11
c) Ishumi elinambini
d) Ngama-13