Rarangi ti'aturi me nga rarangi motuhake: whakamaramatanga, tauira

I roto i tenei whakaputanga, ka whakaarohia he aha te huinga raina o nga aho, te ti'aturi raina me te aho motuhake. Ka hoatu ano e matou etahi tauira mo te pai ake o te mohio ki nga kaupapa kaupapa.

Te Tautuhinga Rarangi Whakakotahitanga o nga Aho

Rarangi huinga (LK) wā s₁ki te₂, …, s_n Tuhinga A ka karangahia he whakaaturanga o te ahua e whai ake nei:

αs₁ + αs₂ + … + αs_n

Mena he whakarea katoa α_i he rite ki te kore, no reira ko te LC iti. Arā, he ōrite te huinga rārangi iti ki te haupae kore.

Hei tauira: 0 · s₁ + 0 · s₂ + 0 · s₃

Na reira, ki te iti rawa tetahi o nga whakarea α_i kaore i te rite ki te kore, katahi ko te LC kore noa.

Hei tauira: 0 · s₁ + 2 · s₂ + 0 · s₃

Rarangi ti'aturi me nga rarangi motuhake

Ko te punaha aho ti'aturi rārangi (LZ) mena he huinga rarangi kore-iti o aua mea, he rite ki te raina kore.

No reira ka taea e te LC kore-iti i etahi wa ka rite ki te aho kore.

Ko te punaha aho motuhake rārangi (LNZ) mena he rite te LC iti ki te aho null.

Notes:

• I roto i te matrix tapawha, he LZ te punaha haupae mena he kore noa te whakatau o tenei matrix (te = 0).
• I roto i te matrix tapawha, ko te punaha haupae he LIS mena karekau te whakatau o tenei matrix i te rite ki te kore (te ≠ 0).

He tauira o te raruraru

Kia kimihia mena ko te punaha aho {s₁ = {3 4};s₂ = {9 12}} ti'aturi rārangi.

Te whakatau:

1. Tuatahi, me hanga he LC.

α₁{3 4} + a₂{9 12}.

2. Inaianei kia mohio tatou he aha nga uara me tango α₁ и α₂kia rite te huinga rarangi ki te aho null.

α₁{3 4} + a₂{9 12} = {0 0}.

3. Me hanga he punaha wharite:

4. Wehea te whārite tuatahi ki te toru, te tuarua ki te whā:

5. Ko te otinga o tenei punaha he aha α₁ и α₂, Me α₁ = -3a₂.

Hei tauira, mena α₂ = 2ka α₁ =-6. Ka whakakapihia e matou enei uara ki te punaha o nga wharite o runga ake nei ka whiwhi:

whakahoki: na nga rarangi s₁ и s₂ ti'aturi rārangi.