TUGAS I ALJABAR LINIER D.docx

8/17/2019 TUGAS I ALJABAR LINIER D.docx

1/4

TUGAS I ALJABAR LINIER

OLEH:

NAMA : HARTINA HUSAIN

NIM : H12113005

KELAS : D

PRODI STATISTIKA

JURUSAN MATEMATIKA

FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM

UNIVERSITAS HASANUDDIN

2014


2/4

Soal

1. M!al"a# P3 a$ala% %&'(#a# 'ol#o& )*+$*+a,a- 3 a#/ -*+-(-('

-*+%a$a' o'*+a! -a&)a% $a# o'*+a! '*+"ala# !ala+. P*+"!a

a'a"a% %&'(#a# 'ol#o& )*+)*#-(" a0a2a22a33 &*+('a"a#

!() +(a#/ $a+ P3. Jaa) :M!al"a# a0a2a22a33 &*+('a"a# !()%&'(#a# $a+

!*)(a% P3 &a"a $#a&a"a# !()+(a#/6subspace 7 P3.Sa+a- a0a2a22a33 $!*)(- !()+(a#/ $a+ P3 a$ala% :

1. W ≠ 8 92. W ⊆ P3

W vu ∈, W vu ∈+

3. J"a &a"a

W uk ∈ W u ∈

4. J"a $a# k ∈ Rl &a"a

Bukti :1. )("a# %&'(#a# "o!o#/ "a+*#a

∀ a0

, a2

, a3∈W dimana a

0, a

2, a

3 ∈ R . o#-o%#a 2332;3.

2. J*la! )a%a W ⊆ P3

3. A&)l !*&)a+a#/ (


3/4

2. M!al"a# $"*-a%( &a-+"! 22:D&a#a :

A [3 20 1] > [ 0 2−2 4 ] [ 1 1−2 5 ] D

[ 4 5−2 10]A'a"a% &a-+"! D $a'a- $-(l! !*)a/a "o&)#a! l#*+ $a+ A<

$a# ? Jaa) :

Ma-+"! D $"a-a"a# "o&)#a! l#*+ $a+ A $a# ,"a &*&*#(% :

D22 "1.A22"2.>22"3.22

D&a#a "1


4/4

[3

2

0

0 1

2 1

−2 −21 4 5 ]

[k

1

k 2k

3]

[ 4

5

−2

10 ]D*#/a# O>E $a'a- "-a '*+ol*% :

[ 3 0 1 4

2 2

0 −21 4

1 5

−2 −25 10

] B1( 13 )[ 1 0 1/3 4 /3

2 2

0 −21 4

1 5

−2 −25 10

]B21 (−2 )

B41

(−1 )[ 1 0 1/3 4 /30 2

0 −20 4

1/3 7 /3−2 −2

14 /3 26 /3] B 2(12 ) [ 1 0 1/3 4 /30 1

0 −20 4

1/6 7/6−2 −2

14 /3 26 /3 ]B32(2)

B42(−4)[

1 0 1/3 4/3

0 1

0 0

0 0

1/6 7 /6−5/3 1/3

4 4] B3(−35 ) [

1 0 1/3 4/3

0 1

0 0

0 0

1/6 7 /61 −1/5

4 4]

B43(−4)[

1 0 1/3 4 /3

0 1

0 0

0 0

1/6 7 /61 −1/50 24/5

]Ka+*#a >a+! -*+a"%+ 'a$a &a-+"! # &*#(#,(""a# )a%a S!-*&

'*+!a&aa# l#*a+ 6SPL7 -*+!*)(- a$ala% -$a" "o#!!-*# 6-$a"

&*&'(#a !ol(! 7. Ja$< -$a" a$a #la "1< "2< $a# "3 a#/

&*&*#(% !*%#//a tidak dapat din!atakan sebagaik"mbinasi #inear dari A$B dan %.

Documents

TUGAS I ALJABAR LINIER D.docx