Nemo matrix juzu'i

A cikin wannan ɗaba'ar, za mu yi la'akari da abin da matrix mai juzu'i yake, kuma, ta yin amfani da misali mai amfani, za mu bincika yadda za a iya samun ta ta amfani da tsari na musamman da algorithm don ayyuka masu zuwa.

Ma'anar matrix mai juyayi

Da farko, bari mu tuna menene ma'anar lissafin lissafi. Sai mu ce muna da lamba 7. Sa'an nan kuma sabaninsa zai zama 7^-1 or ¹/₇. Idan ka ninka waɗannan lambobi, sakamakon zai zama ɗaya, watau 7 7^-1 = 1.

Kusan iri ɗaya tare da matrices. Juya baya Ana kiran irin wannan matrix, ninka wanda ta hanyar asali, muna samun ainihin ɗaya. Ana mata lakabi da A^-1.

A · A^-1 =E

Algorithm don nemo matrix juzu'i

Don nemo matrix mai juzu'i, kuna buƙatar samun damar ƙididdige matrix, da kuma samun ƙwarewar yin wasu ayyuka tare da su.

Ya kamata a lura nan da nan cewa ana iya samun inverse ɗin don matrix square kawai, kuma ana yin wannan ta amfani da dabarar da ke ƙasa:

|A| - ƙaddarar matrix;

A^T_M shine matrix da aka jujjuya na kari na algebra.

lura: idan mai ƙididdigewa ba shi da sifili, to, matrix mai juzu'i ba ya wanzu.

Example

Bari mu nemo matrix A a kasa akwai juyi da shi.

Magani

1. Da farko, bari mu nemo mai ƙayyade matrix ɗin da aka bayar.

2. Yanzu bari mu yi matrix mai girma iri ɗaya da na asali:

Muna buƙatar gano waɗanne lambobi ya kamata su maye gurbin asterisks. Bari mu fara da ɓangaren hagu na sama na matrix. Ana samun ƙarami zuwa gare ta ta hanyar ketare layi da ginshiƙan da yake ciki, watau a cikin duka biyun a lamba ɗaya.

Adadin da ya rage bayan yajin aiki shine ƙaramar da ake buƙata, watau M₁₁ = 8.

Hakazalika, muna samun ƙananan yara don sauran abubuwan da ke cikin matrix kuma muna samun sakamako mai zuwa.

3. Mun ayyana matrix na algebraic kari. Yadda za a lissafta su don kowane kashi, mun yi la'akari a cikin wani dabam.

Misali, ga wani kashi a₁₁ Ana ɗaukar ƙarin algebra kamar haka:

A₁₁ = (-1)^{1 + 1} M₁₁ = 1 · 8 = 8

4. Yi jujjuyawar matrix da aka samu na kari na algebra (watau musanya ginshiƙai da layuka).

5. Ya rage kawai don amfani da dabarar da ke sama don nemo matrix juzu'i.

Za mu iya barin amsar a cikin wannan nau'i, ba tare da raba abubuwan da ke cikin matrix ta lamba 11 ba, tun da yake a cikin wannan yanayin muna samun lambobi masu banƙyama.

Duba sakamakon

Don tabbatar da cewa mun sami inverse na asali matrix, za mu iya samun samfurin su, wanda ya kamata daidai da ainihi matrix.

A sakamakon haka, mun sami matrix na ainihi, wanda ke nufin mun yi komai daidai.