Ruang Vektor: Pendekatan formal Edi Cahyono Jurusan Matematika FMIPA Universitas Haluoleo Kendari..::.. Indonesia.

Presentasi berjudul: "Ruang Vektor: Pendekatan formal Edi Cahyono Jurusan Matematika FMIPA Universitas Haluoleo Kendari..::.. Indonesia."— Transcript presentasi:

1 Ruang Vektor: Pendekatan formal Edi Cahyono edi_cahyono@innov-center.org Jurusan Matematika FMIPA Universitas Haluoleo Kendari..::.. Indonesia

2 Definisi Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia V : himpunan tak kosong, dan terdapat operasi penjumlahan dan perkalian dengan skalar. V dikatakan ruang vektor bila aksioma-aksioma berikut dipenuhi.

3 Aksioma-aksioma Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia 1 2 3 4 5

4 Aksioma-aksioma Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia 6 7 8 9 10

5 Teorema Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia

6 Bukti a ) Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia Aksioma 4 Aksioma 5 Aksioma 3 Aksioma 8 Sifat penjumlahan bil. Real Aksioma 5

7 Definisi Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia V : ruang vektor dan W dikatakan sub ruang dari V bila W ruang vektor dengan operasi seperti pada V.

8 Teorema Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia

9 Definisi Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia

10 Teorema Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia

11 Bukti a ) Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia 1) 2) 3) Ini membuktikan W subruang dari V.

12 Bukti b ) Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia Ini membuktikan W himpunan bagian dari V.

13 Definisi Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia

14 Teorema Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia

15 Definisi Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia

16 Teorema Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia

17 Teorema Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia

18 Teorema Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia

19 Definisi Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia

20 Teorema Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia

21 Department of Mathematics Universitas Haluoleo Kendari..::.. Indonesia