Matriks
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The document discusses different types of matrices including: 1) Row matrices which have 1 row and multiple columns. 2) Column matrices which have 1 column and multiple rows. 3) Rectangular matrices which have a different number of rows and columns. 4) Square matrices which have the same number of rows and columns. It also describes how to add and subtract matrices provided they are the same order, and how to find the transpose of a matrix by switching the rows and columns.
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www.StokeNewingtonHistory.com
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Matriks
- 1. By : Anik Safitri, S.Pd
- 2. Susunan bilangan yang diletakkan dalam kurung biasa () atau kurung siku [] dan diatur menurut aturan baris dan kolom dalam suatu jajaran berbentuk persegi dan persegi panjang
- 3. A= 3 1 5 9 2 1 3 7 0 1 2 3 Nama Poin Sesi 1 Poin Sesi 2 Poin Sesi 3 Jumlah Poin An 3 1 5 9 In 2 1 3 7 Un 0 1 2 3 Jumlah baris : Jumlah kolom : 3 4 ORDO 𝐴3×4
- 4. 3 1 −2 5 2 0 𝐴3×2= 𝑎𝑖𝑗 = Elemen pada baris i kolom j 𝑎12 = 1 𝑎21 = −2 𝑎32 = 0
- 5. 1. Matriks Baris Matriks yang hanya terdiri dari 1 baris (Ordo 1 x n) Contoh : 𝐴1×3 = 3 1 7 2. Matriks Kolom Matriks yang hanya terdiri dari 1 kolom (Ordo m x 1) Contoh : 𝐴3×1 = 4 3 8
- 6. 3. Matriks Persegi Panjang Matriks yang banyak barisnya tidak sama dengan banyak kolom (Ordo m x n) 𝐶2×3 = 1 5 4 −3 1 0 4. Matriks Persegi Matriks yang banyak barisnya sama dengan banyak kolom (Ordo n x n) 𝐷3×3 = 2 9 5 −2 0 3 1 5 −4 trace (jumlah elemen pada diagonal utama)= 2+0+(-4) = -2
- 7. 5. Matriks nol (O) Matriks yang semua elemennya bernilai 0 (nol) 𝑂3×3 = 0 0 0 0 0 0 0 0 0 ; 𝑂2×3 = 0 0 0 0 0 0 6. Matriks diagonal (D) Matriks persegi dengan elemen pada diagonal utama tidak semuanya nol tetapi semua elemen yang lain bernilai nol 𝐷3×3 = 2 0 0 0 7 0 0 0 −5 ; 𝐷3×3 = 0 0 0 0 0 0 0 0 −4
- 8. 7. Matriks Identitas (I) Matriks persegi dengan elemen pada diagonal utamanya 1 dan elemen yang lain 0 𝐼 = 1 0 0 0 1 0 0 0 1 ; 𝐼 = 1 0 0 1
- 9. 8. Matriks segitiga atas Matriks persegi yang elemen di bawah diagonal utamanya bernilai 0. 𝐴 = −3 4 2 0 1 5 0 0 4 9. Matriks segitiga bawah Matriks persegi yang elemen di atas diagonal utamanya bernilai 0. 𝐵 = 1 0 0 5 −6 0 4 6 7
- 10. kolom baris baris kolom 𝐴3×2 = 3 4 7 8 −1 −2 𝐴𝑇 2×3 = 3 7 −1 4 8 −2
- 11. Syarat : 1. Ordo sama 2. Elemen yang bersesuaian nilainya sama 𝐴 = 2 0 9 −1 3 5 ; 𝐵 = 2 1 − 1 32 −1 3 25
- 12. Ordo harus sama. Cara : Menjumlahkan elemen yang bersesuaian 3 4 −2 1 0 5 7 −9 10 + −2 4 1 9 −7 1 1 2 1 = 1 8 −1 10 −7 6 8 −7 11
- 13. 3 4 −2 1 0 5 7 −9 10 − −2 4 1 9 −7 1 1 2 1 = 5 0 −3 −8 7 4 6 −11 9