Ke ngoko, unikwe matrix A = (theij)mxn Ukuhanjiswa kuka-A ngu-At = (a 'ji) nxm.

mna: indawo emgceni
j: indawo yekholamu
unijIsixhobo esikwindawo ij
m: Inani lemiqolo kwimatriki
n: inani leekholamu kwimatriki
Unt: ukuhambisa imatriki ka-A

Qaphela ukuba i-matrix A yeyoku-odola mxn, ngelixa i-transpose yayo engu-At Ye-odolo nx m.

Umzekelo

Fumana imatriki yokuhambisa yematriki B.

Njengoko imatriki enikiweyo inguhlobo lwe-3 × 2 (imiqolo emi-3 kunye neekholamu ezi-2), ukutshintsha kwayo kuya kuba luhlobo 2 × 3 (2 imiqolo kunye neekholamu ezi-3).
Ukwakha i-matrix yokuhambisa, kufuneka sibhale zonke iikholamu zika-B njengemigca ka-Bt. Njengoko kubonisiwe kulo mzobo ulandelayo:

Ke ngoko, i-matrix yokudlulisa ka-B iya kuba:

bona kwakhona: Ukufika

## Iipropathi zetranspose matrix

• (At)t = A: le propati ibonisa ukuba ukuhanjiswa kwematriki etshintshiweyo sisiseko sokuqala.
• (A + B)t = At + BtIsambuku sokudityaniswa kwematriki ezimbini siyalingana nesixa sokutshintshwa komnye nomnye.
• (A. B)t = Bt . unt: Ukutshintsha kokuphindaphindwa kwematriki ezimbini kulingana nemveliso yotshintsho nganye nganye, ngokulandelelana.
• (M) = umz (MtUkumiselwa kwematriki eguqulweyo kuyafana nokuchazwa kwematriki yoqobo.

## Imatriki ehambelanayo

Imatriki ibizwa ngokuba lulingano xa, kuyo nayiphi na into ye matrix A, ukulingana aij = aji ewe

Imatriki zolu hlobo ziimatriki zesikwere, oko kukuthi, inani lemiqolo lilingana nenani leekholamu.

Imatriki nganye ehambelanayo iyanelisa ulwalamano olulandelayo:

A = At

## Imatriki echaseneyo

Kubalulekile ukuba ungabhidanisi imatriki echaseneyo ne-transpose. Imatriki echaseneyo yenye equlathe izinto ezifanayo kwimiqolo nakwiikholamu, nangona kunjalo, ineempawu ezahlukileyo. Ke ngoko, isichasi se-B ngu-B.

## Imatriki eguqulweyo

I-matrix eguqulweyo (iboniswe linani -1) yenye imveliso yeematriki ezimbini ilingana nesazisi (mat) sodweliso olufanayo.

Umzekelo:

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

## Ukuzivocavoca umzimba ngeempendulo

1. (Fei-SP) Ngenxa yematriki A =, apho uAt Ukutshintsha kwayo, ukumiselwa kwematriki A. At :

a) Ngama-1
b) 7
c) Ishumi elinambini
d) Ngama-49

2. (FGV-SP) A no-B likomkhulu kunye no-At Ngaba i-transpose matrix ka-A. Ukuba, emva koko yi-matrix At . B ayizukusebenza:

a) x + y = -3
b) x. y = 2
c) x / y = -4
d) x. kwaye2 = -1
e) x / y = -8

3. (UFSM-RS) Ukwazi ukuba i-matrix

lilinganisa ukuhambisa, ixabiso le-2x + y ngu:

a) -23
b) -11
c) -1
d) Ngama-11
e) Ama-23