tugas i aljabar linier d.docx
TRANSCRIPT
-
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
-
8/17/2019 TUGAS I ALJABAR LINIER D.docx
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#/ (
-
8/17/2019 TUGAS I ALJABAR LINIER D.docx
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
-
8/17/2019 TUGAS I ALJABAR LINIER D.docx
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 %.