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Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 2 of 132 Go Back Full Screen Close Quit Rencana materi yang akan dibahas dalam kelas adalah: • Lapangan dan Ruang Vektor. • Ruang-bagian Vektor. • Himpunan Pembentang, Bebas linier dan Basis. • Dimensi, Jumlahan Langsung, Koordinat dan Basis Terurut. • Pemetaan linier pada Ruang Vektor. • Pemetaan linier dan <strong>Aljabar</strong> matriks. • Perubahan dari Basis. • Rank, Determinan dan Invers. • Bentuk Echelon dari suatu Matriks. • Eigenvektor dan Eigenvalue. • Orthogonalitas (Proses Orthogonalitas Gram-Schmidt). • General Invers.
Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 3 of 132 Go Back Full Screen Close Quit Lapangan(Field) Suatu lapangan adalah suatu himpunan K = ∅ bersama-sama dengan dua operasi tambah (+) dan kali (.) sehingga untuk semua a, b, c ∈ K memenuhi: • (a + b) ∈ K (tertutup). • a + b = b + a (komutatif). • (a + b) + c = a + (b + c) (assosiatif). • Ada 0 ∈ K sehingga a + 0 = 0 + a (elemen netral). • Ada suatu −a ∈ K sehingga a + (−a) = −a + a = 0 (invers). • (a.b) ∈ K (tertutup). • a.b = ba (komutatif). • (a.b).c = a.(b.c) (assosiatif). • Ada 1 ∈ K sehingga a.1 = 1.a = a (elemen identitas). • Bila a = 0, maka ada a −1 ∈ K sehingga a.a −1 = a −1 .a = 1 (invers). • a.(b + c) = (a.b) + (a.c) (distributif).
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