Mizere yodalira komanso yodziyimira payokha: tanthauzo, zitsanzo

M'bukuli, tiwona momwe zingwe zophatikizira zingwe zilili, zingwe zodalirana komanso zodziyimira pawokha. Tidzaperekanso zitsanzo kuti timvetsetse bwino nkhani zanthanthi.

Kutanthauzira Linear Combination of Strings

Linear kuphatikiza (LK) nthawi s₁ndi₂,…,s_n Matrix A amatchedwa mawonekedwe a mawonekedwe awa:

α₁ + izi₂ + ... + izi_n

Ngati ma coefficients onse α_i ndi ofanana ndi zero, kotero LC ndi zochepa. Mwa kuyankhula kwina, kuphatikizika kocheperako kumafanana ndi mzere wa ziro.

Mwachitsanzo: 0 · ndi₁ + 0 · ms₂ + 0 · ms₃

Choncho, ngati mmodzi wa coefficients α_i sikufanana ndi ziro, ndiye LC ndi zosakhala zazing'ono.

Mwachitsanzo: 0 · ndi₁ + 2 · ms₂ + 0 · ms₃

Mizere yodalira ndi yodziyimira payokha

The string system ndi modalira (LZ) ngati pali kuphatikizika kosawerengeka kwa mzere wawo, komwe kuli kofanana ndi mzere wa ziro.

Chifukwa chake ndizotsatira kuti LC yopanda pake nthawi zina imakhala yofanana ndi ziro ziro.

The string system ndi linearly palokha (LNZ) ngati LC yaying'ono yokha ndiyofanana ndi chingwe chopanda pake.

Ndemanga:

• Mu matrix a square, mzere wa mzere ndi LZ pokhapokha ngati choyimira cha matrix awa ndi ziro (ndi = 0).
• Mu masikweya matrix, mzere wa mzere ndi LIS pokhapokha ngati choyimira cha matrix sichili chofanana ndi ziro (ndi ≠ 0).

Chitsanzo cha vuto

Tiyeni tifufuze ngati chingwe dongosolo ndi {s₁ = {3 4};s₂ = {9 12}} modalira.

Kusankha:

1. Choyamba, tiyeni tipange LC.

α₁{3 4} + a₂{9 12}.

2. Tsopano tiyeni tipeze zomwe ziyenera kutsatiridwa α₁ и α₂kotero kuti kuphatikiza kwa mzere kufanane ndi chingwe chopanda pake.

α₁{3 4} + a₂{9 12} = {0 0}.

3. Tiyeni tipange dongosolo la ma equation:

4. Gawani equation yoyamba ndi itatu, yachiwiri ndi inayi:

5. Njira yothetsera vutoli ndi iliyonse α₁ и α₂, Ndi α₁ = -3a₂.

Mwachitsanzo, ngati α₂ = 2ndiye α₁ =-6. Timalowetsa zikhalidwezi m'dongosolo la ma equation pamwambapa ndikupeza:

Yankho: kotero mizere s₁ и s₂ modalira.