Sarrus qoidasi - Rule of Sarrus

Sarrus qoidasi: Chapdagi uchta ustunning determinanti pastki o'ng diagonallar bo'ylab hosilalar yig'indisini minus o'ng yuqori diagonallar bo'ylab yig'indisi.

Chiziqli algebrada Sarrus qoidasi a mnemonik qurilma hisoblash uchun aniqlovchi a ${displaystyle 3 imes 3}$ matritsa frantsuz matematikasi nomi bilan atalgan Per Frédéric Sarrus.^[1]

A ni ko'rib chiqing ${displaystyle 3 imes 3}$ matritsa

{displaystyle M = {egin {bmatrix} a_ {11} & a_ {12} & a_ {13} a_ {21} & a_ {22} & a_ {23} a_ {31} & a_ {32} & a_ {33} end {bmatrix }},}

unda uning determinantini quyidagi sxema bo'yicha hisoblash mumkin.

Matritsaning dastlabki ikkita ustunini ketma-ket beshta ustunni berib, uchinchi ustunning o'ng tomoniga yozing. Keyin yuqoridan pastga (qattiq) o'tuvchi diagonallarning mahsulotlarini qo'shing va pastdan yuqoriga (kesikli) o'tayotgan diagonallarning mahsulotlarini ayiring. Bu hosil beradi^[1]^[2]

{displaystyle {egin {aligned} det (M) & = det {egin {bmatrix} a_ {11} & a_ {12} & a_ {13} a_ {21} & a_ {22} & a_ {23} a_ {31} & a_ {32} va a_ {33} oxiri {bmatrix}} [6pt] & = a_ {11} a_ {22} a_ {33} + a_ {12} a_ {23} a_ {31} + a_ {13} a_ { 21} a_ {32} -a_ {31} a_ {22} a_ {13} -a_ {32} a_ {23} a_ {11} -a_ {33} a_ {21} a_ {12} .end {aligned} }}

Muqobil vertikal tartibga solish

Diagonallarga asoslangan shunga o'xshash sxema ishlaydi ${displaystyle 2 imes 2}$ matritsalar:^[1]

{displaystyle det (M) = det {egin {bmatrix} a_ {11} & a_ {12} a_ {21} & a_ {22} end {bmatrix}} = a_ {11} a_ {22} -a_ {21} a_ {12}.}

Ikkalasi ham alohida holatlardir Leybnits formulasi, ammo bu katta matritsalar uchun o'xshash yodlash sxemalarini bermaydi. Sarrus qoidasi, yordamida ham olinishi mumkin Laplas kengayishi a ${displaystyle 3 imes 3}$ matritsa.^[1]

Sarrus qoidasini o'ylashning yana bir usuli bu matritsaning silindrga o'ralganligini tasavvur qilish, o'ng va chap qirralarning birlashtirilishi.

Adabiyotlar

^ ^a ^b ^v ^d Fischer, Gerd (1985). Analytische Geometrie (nemis tilida) (4-nashr). Visbaden: Vieweg. p. 145. ISBN 3-528-37235-4. Sitatda noma'lum parametr bo'sh: | mualliflar = (Yordam bering)
^ Pol Kon: Chiziqli algebra elementlari. CRC Press, 1994 yil, ISBN 9780412552809, p. 69

Tashqi havolalar

Sarrusning Planetmathdagi qoidasi
Lineer Algebra: Determinantlarning Sarrus qoidasi khanacademy.org saytida

[Fischer-1] v ^d Fischer, Gerd (1985). Analytische Geometrie (nemis tilida) (4-nashr). Visbaden: Vieweg. p. 145. ISBN 3-528-37235-4. Sitatda noma'lum parametr bo'sh: | mualliflar = (Yordam bering)

[2] Pol Kon: Chiziqli algebra elementlari. CRC Press, 1994 yil, ISBN 9780412552809, p. 69

[1]

[2]