Reja: Matritsalar. Matritsalarning rangi. Matritsalarni elementar almashtirish. Teskari matritsalar. Matritsa

6- teorema. Satrlariga(ustunlariga) nisbatan zinapoya matritsa ustunlarining(satrlarining) rangi noldan farqli satrlarining(ustunlarining) soniga teng.
7- teorema. Matritsa satrlarining(ustunlarining)rangi matritsa transportirlanganda o’zgarmaydi, ya’ni har qanday P matritsa uchun r_c(H)=r_c(H^T), r_y(H)=r_y(H^T).
Natija. Har qanday matritsa satirlarining rangi ustunlarining rangiga teng.
Teskari matritsalar.
Bizga biror uchinchi tartibli matritsa berilgan bo’lsin.
A=
Uning teskari matritsasini topish uchun matritsani transpartirlaymiz.
Transpartirlash uchun mos ustinlari bilan satirlarini almashtiramiz.
A^T=
Asosiy matritsani determinantini va minorlarini topamiz.
det A=(a₁₁*a₂₂*a₃₃+a₁₃*a₂₁*a₃₂+a₁₂*a₂₃*a₃₁)-(a₁₃*a₂₂*a₃₁+a₁₂*a₂₁*a₃₃+a₁₁*a₂₃*a₃₂)
A₁₁= , A₁₂= , A₁₃=
A₂₁= , A₂₂= , A₂₃= ,
A₃₁= , A₃₂= , A₃₃= .
A^-1= formula bilan aniqlanadi.


Misollar:
1.Matritsaning determinantlarini hisoblang:
1) =(1*9*7+4*0*2+3*5*8)-(8*9*2+1*0*5+3*4*7)=(63+0+120)-(144+0+84)=-45
a)
b)
c)
d)
e)
2. Matritsaning rangini hisoblang:
*4= = = *- = Demak ushbu matritsaning rangi 2 ga teng.

a)

b)
c)
d)
e)
3. Matrisaning teskari matritsasini toping:
1) A= A^-1=?
detA= =(3*0*3+5*8*2+4*1*(-3))- -(4*0*5+3*8*(-3)+3*1*2)=(0+80-12)-(0-72+6)=68+66=134
A₁₁= =0*3-(-3)*8=24 A₁₂= =1*3-5*8=-21 A ₁₃= =1*(-3)-5*0=-8 A₂₁= =2*3-(-3)*3=15 A₂₂= =3*3-5*4=-11 A ₂₃= =3*(-3)-5*2=-19
A₃₁= =2*8-0*4=16 A₃₂= =3*8-1*4=20 A ₃₃= =3*0-1*2=-2
A^-1= = =
a)
b)
c)
d)
e)
4. Quyidagi tenglamalarni yeching:
1) A*x=B 2) x*A=B 3) A*x*B=C
x=A^-1*B x=B*A^-1 x=A^-1*B^-1*C
A= B= C=
x=A^-1*B^-1*C= = = =

1. 
   A= B= C=
   
2. 
   A= B= C=