Linear inotsamira uye yakazvimirira mitsara: tsananguro, mienzaniso

Muchinyorwa chino, tichatarisa kuti chii chinonzi mutsara musanganiswa wetambo, mutsara unotsamira uye wakazvimirira tambo. Isu tinozopawo mienzaniso yekunzwisisa zvirinani zvezvinyorwa zvedzidziso.

Kutsanangura Linear Combination yeTrings

Linear musanganiswa (LK) nguva s₁ne₂, ..., p_n matrix A inonzi chirevo chechimiro chinotevera:

α₁ + αs₂ + ... + αs_n

Kana ese coefficients α_i akaenzana ne zero, saka LC iri zvishoma. Nemamwe manzwi, musanganiswa wemutsara usingakoshi unoenzana ne zero row.

Semuyenzaniso: 0 · p₁ + 0 · p₂ + 0 · p₃

Saizvozvo, kana kanenge imwe chete coefficients α_i haina kuenzana ne zero, saka LC iri isiri-nhando.

Semuyenzaniso: 0 · p₁ + 2 · p₂ + 0 · p₃

Linearly inotsamira uye yakazvimirira mitsetse

Iyo tambo system ndeye linearly dependent (LZ) kana paine musanganiswa wemutsara usiri wemutsetse wavo, wakaenzana nemutsara we zero.

Saka zvinotevera kuti isiri-yadiki LC inogona mune dzimwe nguva kuenzana ne zero tambo.

Iyo tambo system ndeye linearly yakazvimirira (LNZ) kana chete diki LC yakaenzana netambo isina maturo.

Notes:

• Mune sikweya matrix, iyo mutsara sisitimu iLZ chete kana chirevo cheiyi matrix chiri zero (ari = 0).
• Mune sikweya matrix, iyo mutsara sisitimu ndeye LIS chete kana chirevo cheiyi matrix isina kuenzana ne zero (ari ≠ 0).

Muenzaniso wedambudziko

Ngationei kana tambo system iri {s₁ = {3 4};s₂ = {9 12}} linearly dependent.

Sarudzo:

1. Kutanga, ngatiite LC.

α₁{3 4} + a₂{9 12}.

2. Zvino ngationei kuti ndezvipi zvakakosha zvinofanirwa kutora α₁ и α₂kuitira kuti musanganiswa wemutsara uenzane netambo isina maturo.

α₁{3 4} + a₂{9 12} = {0 0}.

3. Ngatiite hurongwa hwemaequation:

4. Kamura equation yekutanga netatu, yechipiri neina:

5. Mhinduro yegadziriro iyi ndeipi α₁ и α₂, Ne α₁ = -3a₂.

Semuenzaniso, kana α₂ = 2ipapo α₁ =-6. Isu tinotsiva izvi zvakakosha muhurongwa hweequations pamusoro uye titore:

Pindura: saka mitsetse s₁ и s₂ linearly dependent.