Matriks adalah sekumpulan bilangan yang disusun secara baris dan kolom dan ditempatkan pada kurung biasa atau kurung siku.
Penulisan matriks:

atau
Ordo suatu matriks adalah bilangan yang menunjukkan banyaknya baris (m) dan banyaknya kolom (n).

Matriks di atas berordo 3x2.
Beberapa contoh dari jenis-jenis matriks :
Matriks Identitas (I)
Matriks identitas (I)adalah matriks yang nilai-nilai elemen pada diagonal utama selalu 1.

Matriks Transpose (At)
Matriks transpose adalah matriks yang mengalami pertukaran elemen dari baris menjadi kolom dan sebaliknya. Contoh:

maka matriks transposenya (A
t) adalah

Operasi perhitungan pada matriks
Kesamaan 2 matriks
2 matriks dikatakan sama jika ordonya sama dan elemen yang seletak sama.
Contoh:

Tentukan nilai 2x-y+5z!
Jawab:
maka 
maka 
maka 



Penjumlahan matriks
2 matriks bisa dijumlahkan jika ordonya sama dan penjumlahan dilakukan dengan cara menjumlahkan elemen yang seletak.
Contoh:

Pengurangan matriks
2 matriks bisa dikurangkan jika ordonya sama dan pengurangan dilakukan dengan cara mengurangkan dari elemen yang seletak.
Contoh:

Perkalian bilangan dengan matriks
Contoh:

Perkalian matriks
2 Matriks dapat dikalikan jika jumlah baris matriks A = jumlah kolom matriks B.
Penghitungan perkalian matriks:
Misalkan:

dan

maka

Contoh:

Determinan suatu matriks
Matriks ordo 2x2
Misalkan:

maka Determinan A (ditulis

) adalah:

Matriks ordo 3x3
Cara Sarrus
Misalkan:
Jika

maka tentukan

!

Penghitungan matriks dilakukan dengan cara menambahkan elemen dari kiri atas ke kanan bawah (mulai dari a → e → i, b → f → g, dan c → d → h) lalu dikurangi dengan elemen dari kanan atas ke kiri bawah (mulai dari c → e → g, a → f → h, dan b → d → i) sehingga menjadi:

Contoh:

maka tentukan

!


Cara ekspansi baris-kolom
Misalkan:
Jika

maka tentukan

dengan ekspansi baris pertama!


Matriks Singular
Matriks singular adalah matriks yang nilai determinannya 0.
Contoh:

Jika A matriks singular, tentukan nilai x!
Jawab:


vs 
Invers matriks
Invers matriks 2x2
Misalkan:

maka inversnya adalah:

Sifat-sifat invers matriks




Persamaan matriks
Tentukan X matriks dari persamaan:
- Jika diketahui matriks A.X=B




- Jika diketahui matriks X.A=B




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