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

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

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

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

5. Contoh 1: Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Contoh 1:

6. Bukti: Aksioma 1 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 1

7. Bukti: Aksioma 2 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 2

8. Bukti: Aksioma 3 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 3

9. Bukti: Aksioma 4 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 4

10. Bukti: Aksioma 5 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 5

11. Bukti: Aksioma 6 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 6

12. Bukti: Aksioma 7 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 7

13. Bukti: Aksioma 8 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 8

14. Bukti: Aksioma 9 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 9

15. Bukti: Aksioma 10 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 10

16. Contoh 2: Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Contoh 2:

17. Bukti: Aksioma 1 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 1

18. Bukti: Aksioma 2 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 2

19. Bukti: Aksioma 3 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 3

20. Bukti: Aksioma 4 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 4

21. Bukti: Aksioma 5 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 5

22. Bukti: Aksioma 6 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 6

23. Bukti: Aksioma 7 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 7

24. Bukti: Aksioma 8 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 8

25. Bukti: Aksioma 9 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 9

26. Bukti: Aksioma 10 Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Bukti:
Aksioma 10

27. Contoh 3: Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Contoh 3:

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

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

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

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

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

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

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

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

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

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

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

39. Contoh Universitas Haluoleo Department of Mathematics
Kendari ..::.. Indonesia
Contoh

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

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

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

43. Creating Math for better living
Department of Mathematics
Universitas Haluoleo
Kendari ..::.. Indonesia
Creating Math for better living
Thank you