Gabarito ApostilaI INFA43

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CENTRO UNIVERSITÁRIO CARIOCA ÁLGEBRA LINEAR – INF A43 
 
Gabarito – Apostila – Unidade I 
 
1) 
a) )13,21,18()16,0,12()3,21,6()4,0,3.(4)1,7,2.(343 −−=−−−=−−−=− vu rr 
b) 
)26,39,5()40,25,0()12,0,9()2,14,4()8,5,0.(5)4,0,3.(3)1,7,2.(2532 −−−=−−+−=−−−+−=−+ wvu rrr
 
2) 
a) 
1323
2
=→=+→=+
=
yyyx
x
 
 
b) 
62.33
242
==→=
=→=
yxy
xx
 
 
3) 
a) )0,0,1.()0,1,1()1,1,1.()4,3,2( zyx ++=− 
),,()4,3,2(
)0,0,()0,,(),,()4,3,2(
xyxzyx
zyyxxx
+++=−
++=−
 





=
−=−−=→−=+
−=+−−=→=++
4
7433
92742
x
yyx
zzyx
 
 
 
4) 
a) 
201252
0)4,5,2()3,,1(
−=→=−−=
=−−=
kkvu
kvu
r
o
r
o
r
o
r
 b) 
0012312
0)3,1,6()4,3,2(
=→=−−=
=−−=
kkvu
kvu
r
o
r
o
r
o
r
 
 
 
5) 
a) 53)7(2 22 =−+=ur b) 13169)4()12(3 222 ==−+−+=ur 
 
 
6) 





−=
−
==
53
7
,
53
2
53
)7,2(
u
u
uu r
r
r
 b) 





−−=
−−
==
13
4
,
13
12
,
13
3
13
)4,12,3(
u
u
uu r
r
r
 
 
7) 
a) )1,5()5,2()4,3( −−=−−=−=
→
ABAB b) )7,2,5()4,2,1()3,0,6( −=−−−=−=
→
ABAB 
 
8) wvu rrr =+2 
1132
)4,1()4,32(
)4,1()2,3()2,2(
)4,1()2,3()1,(2
−=∴=+⇒
=+
=+
=+
aa
a
a
a