Ulawulo Cramer kunye nesicelo yayo

ulawulo Cramer kaThixo - yenye yeendlela ngqo ukuxazulula iinkqubo kwizibalo yomgama aljibra (Slough). Ukuchaneka kwayo ngenxa yokusetyenziswa izezona kwinkqubo isizalo, kwakunye ezinye izithintelo ezibekwe ngayo ubungqina theorem.

Inkqubo quadratic yomgama aljibra kunye okuza alunge, umzekelo, nobuninzi R - amanani yokwenene angaziwa x1, x2, ..., xn yingqokelela amabinzana

ai2 x1 + ai2 x2 + ... grafu xn = bi na i = 1, 2, ..., m, (1)

apho aij, bi - amanani ngokwenene. Ngalinye le ntetho kuthiwa quadratic yomgama, aij - okuza le angaziwa, bi - okuza ezizimeleyo kwizibalo.

nesisombululo (1) ekubhekiselelwe n-mbini kumda wesangqa x ° = (x1 °, x2 °, ..., xn °), apho kufakwe inkqubo ukuba angaziwa x1, x2, ..., xn, ngamnye imigca kwinkqubo uba equation best .

Le nkqubo ibizwa iyavumelana ukuba unalo isisombululo enye ubuncinane, kwaye awuhambelani, ukuba udibana isicombululo isethi isethi engenanto.

Kufuneka kukhunjulwe ukuba ukuze sifumane izisombululo iinkqubo quadratic kumgama owazisayo usebenzisa indlela Cramer, iinkqubo matrix kufuneka ukuba isikwere, nto leyo lithetha inani elifanayo angaziwa kunye zibalo kule nkqubo.

Ngoko ke, ukuba usebenzise indlela Cramer kaThixo, wena ubuncinane kufuneka bazi ukuba yintoni na matrix inkqubo quadratic yomgama-aljibra, kwaye ikhutshwe. Kwaye okwesibini, ukuba baqonde into ibizwa ngokuba onefuthe ngayo isizalo nezakhono zayo ikhompyutha.

Makhe sicinge ukuba olu lwazi onazo. Iyamangalisa! Emva koko kufuneka ngentloko nje ifomula emisela indlela Kramer. Ukuze lula ukuba ukhumbule ukusebenzisa nobhalo zilandelayo:

• Det - le onefuthe engundoqo isizalo kwenkqubo;

• deti - yeyona ye isizalo efunyenwe matrix lokuqala kwenkqubo ngokubuyisela i column i-th ka isizalo ukuya kumda wesangqa ikholam ogama Izakhi kumacala ilungelo quadratic linear algebra;

• n - inani angaziwa kunye zibalo kule nkqubo.

Emva koko ulawulo intelekelelo Cramer kaThixo i-th Icandelo xi (i = 1, .. n) n-mbini esiyua x angabhalwa

xi = deti / Det, (2).

Kulo mzekelo, Det eyahlukileyo ngokungqongqo ukusuka kwiqanda.

Ukohluka yesisombululo kwenkqubo xa kankqoyi inikwa imeko ukungalingani le onefuthe ephambili nkqubo ku nothi. Kungenjalo, ukuba sum of (xi), kabini, ngqongqo ezintle, ngoko SLAE matrix sigcawu infeasible. Oku kwenzeka ingakumbi xa ubuncinane enye nonzero deti.

Umzekelo 1. Ukusombulula le nkqubo-ntathu xu usebenzisa ifomula Cramer kaThixo.
2 x1 + x2 + x3 = 31 4,
5 x1 + x2 + x3 = 2 29,
3 x1 - x2 + x3 = 10.

Isigqibo. Thina bhala phantsi matrix inkqubo kaloliwe ngolutya, apho iAyi - ke i-th umqolo we isizalo.
A1 = (1 2 4), A2 = (5 1 2), A3 = (3, -1, 1).
Column okuza ezamahala b = (31 Oktobha 29).

Inkqubo engundoqo Det onefuthe
DET = a11 a22 a33 + a12 a23 a31 + a31 a21 a32 - a13 a22 a31 - a11 a32 a23 - a33 a21 a12 = 1 - 20 + 12 - 12 + 2 - 10 = -27.

Ukubala lobeko det1 usebenzisa a11 = B1, a21 = B2, a31 = B3. ke
det1 = B1 a22 a33 + a12 a23 b3 + a31 B2 a32 - a13 a22 b3 - B1 a32 a23 - a33 B2 a12 = ... = -81.

Ngokufanayo, ukuba olunokubalwa det2 ukusetyenziswa endaweni a12 = B1, a22 = B2, a32 = B3, yaye, ngokunjalo, ukubala det3 - a13 = B1, a23 = B2, a33 = B3.
Ngolo hlobo unako ukubona ukuba det2 = -108, kunye det3 = - 135.
Ngokutsho iifomyula Cramer ukufumana x1 = -81 / (- 27) = 3, x2 = -108 / (- 27) = 4, x3 = -135 / (- 27) = 5.

Impendulo: x ° = (3,4,5).

Ukuthembela nokusebenza kwalo mgaqo, indlela yokusombulula Kramer kweenkqubo quadratic yomgama zingasetyenziswa ngokungangqalanga, umzekelo, ukuba aphande inkqubo kwinani kwezisombululo kuxhomekeke ixabiso k parameter kunokwenzeka.

Umzekelo 2. Ukuze ubone oko amaxabiso i parameter k ukungalingani | TE - y - 4 | + | x + ky + 4 | <= 0 uye ngqo isisombululo enye.

Isigqibo.
Le ukungalingani, yi kwenkcazo umsebenzi umnqongo iya kwenziwa kuphela ukuba zombini magama zero ngaxeshanye. Ngoko ke, le ngxaki kuyehla ukuze sifumane isisombululo kwizibalo linear algebra

TE - y = 4,
x + ky = -4.

Isisombululo kule nkqubo kuphela ukuba yeyona iphambili le
DET = k ^ {2} + 1 nonzero. Kucacile ukuba le meko lanelisekile ukuba onke amaxabiso yokwenene ye parameter k.

Impendulo: wawo onke amaxabiso yokwenene ye parameter k.

Iinjongo zolu hlobo nazo kuncitshiswa iingxaki ezininzi kwinkalo yemathematika, physics okanye chemistry.