Fontes E Antecedentes Dos Direitos Fundamentais

01) a=A.B

A=[■(1&3&2@2&1&1@-3&-1&0)] B=[■(1&2&3@-2& 3&-4@0&4&2)]

a11=1.1+3.(-2)+2.0=-5 a21=2.1+1.(-2)+1.0=0 a31=(-3).1+(-1).(-2)+0.3=-5

a12=1.2+3.3+2.4=19 a22=2.2+1.3+1.4=11 a32=(-3).2+(-1).3+0.4= -11

a13=1.3+3.(-4)+2.2=-5 a23=2.3+1.(-4)+1.2=4 a33=(-3).3+(-1).(-4)+0.2= -5

a=[■(-5&19&-5@0&11&4@-1&-9&-5)]

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b= B.A

B=[■(1&2&3@-2& 3&-4@0&4&2)] A=[■(1&3&2@2&1&1@-3&-1&0)]

b11=1.1+2.2+3.(-3)=-4 b21= (-2) .1+3.2+(-4).(-3)=16 b31=0.1+4.2+2.(-3)=2

b12=1.3+2.1+3.(-1)=2 b22=(-2).3+3.1+(-4).(-1)=1 b32=0.3+4.1+2.(-1)=2

b13=1.2+2.1+3.0= 4 b23=(-2).2+3.1+(-4).0=-1 b33=0.2+4.1+2.0= 4

b=[■(-4&2&4@16&1&-1@2&2&4)]

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c=A.(C.B)

A=[■(1&3&2@2&1&1@-3&-1&0)] B=[■(1&2&3@-2& 3&-4@0&4&2)] C=[■(2&3&1@5&0&2@1&1&0)]

C.B=

C.B 11=2.1+3.(-2)+1.0=-4 C.B 21= 5.1+0.(-2)+2.0=5 C.B 31=1.1+1.(-2)+0.0=-1

C.B 12=2.2+3.3+1.4=17 C.B 22=5.2+0.3+2.4=18 C.B 32=1.2+1.3+0.4=5

C.B 13=2.3+3.(-4)1.2= -4 C.B 23=5.3+0.(-4)2.2=19 C.B 33=1.3+1(-4)+0.2=-1

A=[■(1&3&2@2&1&1@-3&-1&0)] C.B=[■(-4&17&-4@5&18&19@-1&5&-1)]

A.(C.B)= n

n11=1.(-4)+3.5+2(-1)=9 n21=2.(-4)+1.5+1.(-1)=-4 n31=(-3).(-4)+(-1).5+0.(-1)=7

n12=1.17+3.18+2.5=81 n22=2.17+1.18+1.5=57 n32=(-3).17+(-1).18+0.5=-69

n13=1.(-4)+3.19+2.(-1)=51 n23=2.(-4)+1.19+1.(-1)=10 n33=(-3).(-4)+(-1).19+0.1=-7

A.(C.B)=[■(9&81&51@-4&57&10@7&-69&-7)]

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d) X = 3.A + 2.B – 2.C

A=[■(1&3&2@2&1&1@-3&-1&0)] B=[■(1&2&3@-2& 3&-4@0&4&2)] C=[■(2&3&1@5&0&2@1&1&0)]

X=3.[■(1&3&2@2&1&1@-3&-1&0)] + 2.[■(1&2&3@-2& 3&-4@0&4&2)] -2.[■(2&3&1@5&0&2@1&1&0)]

x=[■(3&9&6@6&3&3@-9&-3&0)] +[■(2&4&6@-4&6&-8@0&8&4)] - [■(4&6&2@10&0&4@2&2&0)]

x=[■(5&13&12@2&9&-5@-9&5&4)] -[■(4&6&2@10&0&4@2&2&0)]

x=[■(1&7&10@-8&9&-9@-11&3&4)]

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2 ) Considerando as matrizes do exercício anterior, calcular:

Det. A b) Det. A.B c) Det. C

a)

Det. A=|■(1&3&2@2&1&1@-3&-1&0)|=|■(1&3&2&1&3@2&1&1&2&1@-3&-1&0&-3&-1)| =

=1.1.0+3.1.(-3)+2.2.1-(2.1.{-3})-(1.1.{-1})-(3.2.0)= -6

Det.A= - 6

b)

Det. A.B

A.B= |■(-5&19&-5@0&11&4@-1&-9&-5)|= |■(-5&19&-5&-5&19@0&11&4&0&11@-1&-9&-5&-1&-9)| =

=(-5).11.(-5)+19.4.(-1)+(-5).0.(-9)-({-5}.11.{-1})-({-5}.4.{-9})-(19.0.{-5})=-36

Det. A.B=-36

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C)

Det. C

C= |■(2&3&1@5&0&2@1&1&0)|= |■(2&3&1&2&3@5&0&2&5&0@1&1&0&1&1)|=

=2.0.0+3.2.1+1.5.1-(1.0.1)-(2.2.1)-(3.5.0)=7

Det.C =7

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3) Calcular o determinante da matriz:

C= [█(2 3 4 -3@ 3 3 5 8@1 3 3 5@3 2 7 9)]=2. |■(3&5&8@3&3&5@2&7&9)|-3. |■(3&5&8@1&3&5@3&7&9)|4. |■(3&3&8@1&3&5@3&2&9)|-(-3). |■(3&3&5@1&3&3@3&2&7)|

2. |■(3&5&8&3&5@3&3&5&3&3@2&7&9&2&7)|=3.3.9+5.5.2+8.3.7-(8.3.2)-(3.5.7)-(5.3.9)=2.11=22

-3.|■(3&5&8&3&5@1&3&5&1&3@3&7&9&3&7)|=3.3.9+5.5.3+8.1.7-(8.3.3)-(3.5.7)-(5.1.9)=(-3).(-10)=30

4. |■(3&3&8&3&3@1&3&5&1&3@3&2&9&3&2)|=3.3.9+3.5.3+8.1.2-(8.3.3)-(3.5.2)-(3.1.9)=4.13=52

-(-3).