Pūnaehana o nā hoohalike algebraic linear

Ma kēia paʻi ʻana, e noʻonoʻo mākou i ka wehewehe ʻana o kahi ʻōnaehana linear algebraic equations (SLAE), pehea kona ʻano, he aha nā ʻano o laila, a pehea hoʻi e hōʻike ai ma kahi ʻano matrix, me kahi mea hoʻonui.

Wehewehe ʻana o kahi ʻōnaehana o nā hoohalike laina

Pūnaehana o nā hoohalike algebraic linear (a i ʻole “SLAU” no ka pōkole) he ʻōnaehana e like me kēia:

• m ka heluna o na hoohalike;
• n ʻo ia ka helu o nā mea hoʻololi.
• x₁,x₂,…, x_n - ʻike ʻole ʻia;
• a₁₁,₁₂…, a_mn - coefficients no ka ike ole;
• b₁na B₂,…, b_m - nā lālā manuahi.

Nā helu helu helu (a_ij) ua hoʻokumu ʻia penei:

• i ka helu o ka hoohalike laina;
• j ʻo ia ka helu o ka hoʻololi i kuhikuhi ʻia e ka coefficient.

Hoʻoholo SLAU - ia mau helu c₁, C₂,…, c_n , ma ka hoonohonoho ana ma kahi o x₁,x₂,…, x_n, e lilo nā hoohalike a pau o ka ʻōnaehana i mau ʻike.

Nā ʻano SLAU

1. Homogene - ua like nā lālā manuahi a pau o ka ʻōnaehana me ka ʻole (b₁ =b₂ = … = b_m = 0).

   

2. ʻO Heterogeneous - inā ʻaʻole i hoʻokō ʻia ke kūlana ma luna.
3. pāhoʻonui – ua like ka heluna o na hoohalike me ka helu o na mea ike ole, ie m = n.

   

4. ʻAʻole maopopo - ʻoi aku ka nui o nā mea i ʻike ʻole ʻia ma mua o ka helu o nā hoohalike.

   

5. hoʻopau ʻia Nui aʻe nā hoohalike ma mua o nā mea hoʻololi.

   

Ma muli o ka nui o nā hoʻonā, hiki ke SLAE:

1. ami loaʻa ma ka liʻiliʻi hoʻokahi hoʻonā. Eia kekahi, inā he ʻokoʻa ia, ua kapa ʻia ka ʻōnaehana definite, inā he nui nā hoʻonā, ua kapa ʻia ʻo ia ka pau ʻole.

   

   He hui ka SLAE ma luna, no ka mea, hoʻokahi wale nō ka hopena: x = 2, y = 3.

2. kūlike ʻole ʻAʻohe hopena o ka ʻōnaehana.

   

   Ua like na aoao akau o na hoohalike, aka, aole like na aoao hema. No laila, ʻaʻohe hopena.

Notation matrix o ka ʻōnaehana

Hiki ke hōʻike ʻia ka SLAE ma ke ʻano matrix:

AX = B

• A ʻO ia ka matrix i hana ʻia e nā coefficients o nā mea ʻike ʻole:

  

• X - kolamu o nā mea hoʻololi:

  

• B - kolamu o nā lālā manuahi:

  

la'ana

Hōʻike mākou i ka ʻōnaehana o nā hoohalike ma lalo nei ma ke ʻano matrix:

Ke hoʻohana nei i nā ʻano i luna, haku mākou i ka matrix nui me nā coefficients, nā kolamu me nā lālā ʻike ʻole a manuahi.

E hoʻopaʻa i ka moʻolelo o ka ʻōnaehana i hāʻawi ʻia ma ke ʻano matrix:

Hoʻonui ʻia SLAE Matrix

Inā i ka matrix o ka ʻōnaehana A hoʻohui i ke kolamu lālā manuahi ma ka ʻākau B, ka hoʻokaʻawale ʻana i ka ʻikepili me kahi pā kūpaʻa, loaʻa iā ʻoe kahi matrix lōʻihi o SLAE.

No ka laʻana ma luna, e like me kēia:

- ka inoa o ka matrix lōʻihi.