Mim ajudem por favor, é pra essa semana, sou pésima em matemática.
Soluções para a tarefa
Resposta:
Explicação passo-a-passo:
1.
A)
6 2
4 3
D= 18-8
D= 10
____
B)
-3 -8
1 2
D= -3.2 -(-8.1)
D= -6 + 8
D= 2
_____
C)
6 10
3 5
D=6.5-(10.3)
D= 30-30
D=0
_____
D)
(1+√5) 3
4 (1-√5)
D= (1+√5).(1-√5) -(3.4)
D= 1-√5+√5-5 - 12
D= 1 - 5 - 12
D= 1 - 17
D = -16
2)
A=
1 3
0 2
B=
-1 3
2 0
Det A.B
[1 3] . [-1 3]
[0 2] . [2 0]
1.(-1)+3.2 1.3+3.0
0.(-1)+2.2 0.3+2.0
-1+6 3
4 0
Det:
5 3
4 0
= 5.0-3.4
= -12
3.
A=
1 0
2 4
Det A(-1)
1 0 (a b) = (1 0)
2 4 (c d) = (0 1)
a b
2a+4c 2b+4d
A = 1 b= 0
2a+4c= 0
2.1+4c= 0
2+4c = 0
4c= -2
C = -1/2
2b+4d= 1
2.0+4d= 1
4d= 1
d = 1/4
1 0
-1/2 1/4
D = 1/4 - 0
D = 1/4
_________
A=
[5]
B =
[-1 2]
[3 -5]
C=
2 -2
3 0
__________
4)
A)
R.: Det A = 5
-------------
B)
Det B
B =
-1 2
3 -5
= 5-6
R.: Det B= -1
__________
C)
Det C
C=
2 -2
3 0
D= 2.0-[-2.3]
D= 0-(-6)
R.: Det C = 6
___________
D)
Det A - Det B
= 5-(-1)
= 5+1
= 6
R.: = 6
----------------------
E)
Det B . Det C
= (-1).6
= - 6
R.: = - 6
----------------
F)
Det [B - C]
B - C
-1 2
3 -5
(-)
2 -2
3 0
=
-1-2 2-(-2)
3-3 -5-0
-3 4
0 -5
D = 15 -0
R.: D = 15
_________
G)
(Det C). B
= 6 x B
B =
-1 2
3 -5
R.:
=
[-6 12]
[18 -30]
________
H)
2.Det B
= 2.(-1)
= -2
R.: = 2
--------------
I)
Det (2B)
2 . B
2 .
-1 2
3 -5
=
-2 4
6 -10
D= 20 - (24)
D = 20-24
R.: D = - 4
___________
J)
Det [I2 + C]
1 0
0 1
(+)
2 -2
3 0
=
3 -2
3 1
D = 3.1 - [(-2).3]
Det = 3 - (-6)
Det = 9
R.: 9
______________
5)
a)
3 2 -1 3 2
5 0 4 5 0
2 -3 1 2 -3
D = 0+16+15-(0-36+10)
D= 31 - (-26)
D = 31+26
R.:
D= 57
----------
B)
2 1 -2 2 1
3 -1 0 3 -1
4 1 -3 4 1
D = 6+0-6-(8+0-9)
D = 0 -(-1)
R.: D = 1
-----------
C)
a 0 0 a 0
0 b a 0 b
0 1 1 0 1
D= ab + 0+0-(0+a^2+0)
R.: D = ab - a^2
-------------------
D)
1 0 a 1 0
0 1 a 0 1
a a 1 a a
D= 1+0+0-(a^2+a^2+0)
D= 1-(2a^2)
R.: D = 1 - a^2
_________
E)
3 5 -1 3 5
0 4 2 0 4
0 0 -2 0 0
D = -24 + 0 - 0 -(0+0+0)
R.: D = - 24
__________
F)
2 2 0 2 0
1 1 1 1 1
4 3 0 4 3
D = 0 + 8 + 0 - (0 +6+0)
D = 8 - 6
R.: D = 2
_______
G)
1 2 0 1 2
1 4 4 1 4
1 8 0 1 8
D = 0+8+0-(0+32+0)
D= 8-32
R.: D= - 24
---------------
H)
3 0 8 3 0
0 7 7 0 7
4 9 0 4 9
D = 0+0+0-(8.7.4+3.7.9+0)
D = -(56.4+21.9)
D = -(224+189)
D = - (413)
R.: D = - 413
___________
I)
0 0 5 0 0
8 10 3 8 10
0 7 4 0 7
D = 0+0+280-(0+0+0)
D= 280
R.: D= 280
____________
J)
a^2 ab b^2 a^2 ab
2a (a+b) 2b 2a (a+b)
1 1 1 1 1
= a^2.(a+b) + ab.2b + b^2.2a
- [b^2.(a+b) + a^2.(2b) + ab.2a]
= a^3 + a^2.b + 2a.b^2+2a.b^2
- [ab^2+b^3+ 2a^2.b+2a^2.b]
= a^3 + a^2.b +4ab^2 - ab^2 - b^3 - 4a^2.b
R.:
= a^3 - 3a^2.b + 3ab^2 - b^3
___________
L)
100 0 0 100 0
0 20 0 0 20
0 0 -30 0 0
= 100.20.(-30) + 0 + 0 - (0 + 0 + 0)
= 2000.(-30)
R.: d = - 60000
________
M)
1 -1 1 1 -1
-1 1 1 -1 1
1 1 -1 1 1
D = -1 -1 - 1 - (1+1-1)
D = - 3 - (-1)
D = -3+1
R.: D = - 2