Respostas
Resposta:
Explicação passo-a-passo:
2)
(X-2a)/3 = (x+ b)/2
2.(x - 2a) = 3.(x+b)
2x - 4A = 3X + 3B
2x - 3x = 3B + 4A
- x = 3B + 4A
X = - 3B - 4A
Ordem : 4 x 5
4 linhas e 5 colunas
a11 a12 a13 a14 a15
a21 a22 a23 a24 a25
a31 a32 a33 a34 a35
a41 a42 a43 a44 a45
Aij = i^4 - j
a11 = 1^4 - 1 = 1 - 1 = 0
a12 = 1^4 - 2 = 1 - 2 = - 1
a13 = 1^4 - 3 = 1 - 3 = - 2
a14 = 1^4 - 4 = 1 - 4 = - 3
a15 = 1^4 - 5 = 1 - 5 = - 4
Aij = i^4 - j
a21 = 2^4 - 1 = 16-1= 15
a22 = 2^4 - 2 = 16 - 2 = 14
a23 = 2^4 - 3 = 16 - 3 = 13
a24 = 2^4 - 4 = 16 - 4 = 12
a25 = 2^4 - 5 = 16 - 5 = 11
Aij = i^4 - j
a31 = 3^4 - 1 = 81 - 1 = 80
a32 = 3^4 - 2 = 81 - 2 = 79
a33 = 3^4 - 3 = 81 - 3 = 78
a34 = 3^4 - 4 = 81 - 4 = 77
a35 = 3^4 - 5 = 81 - 5 = 76
Aij = i^4 - j
a41 = 4^4 - 1 = 256 - 1 = 255
a42 = 4^4 - 2 = 256 - 2 = 254
a43 = 4^4 - 3 = 256 - 3 = 253
a44 = 4^4 - 4 = 256 - 4 = 252
a45 = 4^4 - 5 = 256 - 5 = 251
A =
[0 -1 -2 -3 -4]
[15 14 13 12 11]
[80 79 78 77 76]
[255 254 253 252 251]
b11 b12 b13 b14 b15
b21 b22 b23 b24 b25
b31 b32 b33 b34 b35
b41 b42 b43 b44 b45
Bij = (i^2)^2 + 2j
bij = i^4 + 2j
b11 = 1^4 + 2.1 = 1 +2= 3
b12 = 1^4 + 2.2 = 1 + 4 = 5
b13 = 1^4 + 3^2 = 1+9= 10
b14 = 1^4 + 4^2 = 1 + 16 = 17
b15 = 1^4 + 5^2 = 1 + 25 = 26
bij = i^4 + 2j
b21 = 2^4 + 2.1 = 16+2= 18
b22 = 2^4 + 2.2 = 16+4= 20
b23 = 2^4 + 2.3 = 16 + 6 = 22
b24 = 2^4 + 2.4 = 16 + 8 = 24
b25 = 2^4 + 2.5 = 16 + 10 = 26
bij = i^4 + 2j
b31 = 3^4 + 2.1 = 81+2= 83
b32 = 3^4 + 2.2 = 81 + 4 = 85
b33 = 3^4+ 2.3 = 81+6= 87
b34 = 3^4 + 2.4 = 81+8=89
b35 = 3^4 + 2.5 = 81+10= 91
bij = i^4 + 2j
b41 = 4^4 + 2.1 = 256 + 2 = 258
b42 = 4^4 + 2.2 = 256 + 4 = 260
b43 = 4^4 + 2.3 = 256 + 6 = 262
b44 = 4^4 + 2.4 = 256 + 8 = 264
b45 = 4^4 + 2.5 = 256 + 10 = 266
B =
[3 5 10 17 26]
[18 20 22 24 26]
[83 85 87 89 91]
[258 260 262 264 266]
X = - 3B - 4A
- 3. B
=
[3 5 10 17 26]
[18 20 22 24 26]
[83 85 87 89 91]
[258 260 262 264 266]
-3.3 -3.5 -3.10 -3.17 -3.26
-3.18 -3.20 -3.22 -3.24 -3.26
-3.83 -3.85 -3.87 -3.89 -3.91
-3.258 -3.260 -3.262 -3.264 -3.266
-3B
=
-9 -15 -30 -51 -78
-54 -60 -66 -72 -78
-249 -255 -261 -267 -273
-774 -780 -786 -792 - 798
- 4A
A =
[0 -1 -2 -3 -4]
[15 14 13 12 11]
[80 79 78 77 76]
[255 254 253 252 251]
- 4A
=
-4.0 -4.(-1) -4.(-2) -4.(-3) -4.(-4)
-4.15 -4.14 -4.13 - 4.12 -4.11
-4.80 -4.79 -4.78 -4.77 -4.76
-4.255 -4.254 -4.253 -4.252 -4.251
- 4A
0 4 8 12 16
-60 -56 -52 -48 -44
-320 -316 -312 -308 -304
-1020 - 1016 -1012 -1008 -1004
=
-9 -15 -30 -51 -78
-54 -60 -66 -72 -78
-249 -255 -261 -267 -273
-774 -780 -786 -792 - 798
0 4 8 12 16
-60 -56 -52 -48 -44
-320 -316 -312 -308 -304
-1020 - 1016 -1012 -1008 -1004
=
-9+0 -15+4 -30+8 -51+12 -78+16
-54-60 -60-56 -66-52 -72-48 -78-44
-249-320 -255-316 -261-312 -267-308 -273-304
-774-1020 -780-1016 -786-1012
-792-1008 -798-1004
R.:
[-9 -11 -22 -39 -62]
[-114 -116 -118 -120 -122]
[-569 -571 -573 -575 -577]
[-1794 -1796 -1798 -1800 -1802]
________________
6)
Matriz ordem 2 (2x2)
(A^2 - 2B)^ t
aij = 2i - j
a11 = 2.1 - 1 = 2-1=1
a12 = 2.1 - 2 = 2-2= 0
a21 = 2.2 -1 = 4-1= 3
a22 = 2.2 - 2 = 4 - 2 = 2
A=
1 0
3 2
A^2 = A.A
[1 0] . [1 0]
[3 2] [3 2]
[1.1+0.3 1.0+0.2]
[3.1+2.3 3.0+2.2]
A^2 =
[1 0]
[9 4]
------------
B=
bij =
1 = ( i # j)
3 (i = j)
b11 b12
b21 b22
3 1
1 3
2.B
=
2.3. 2.1
2.1 2.3
6 2
2 6
(A^2 - 2B)^ t
A^2 =
1 0
9 4
(-)
6 2
2 6
1-6 0-2
9-2 4-6
-5 -2
7 -2
[-5 -2]^ t
[7 -2]
=
[-5 7]
[-2 -2]
Transposta
Trocar linha por coluna
Coluna por linha.
R.:
[-5 7]
[-2 -2]
____________
7)
2x + 4y = 4 (:2)
5x - 3y = 4
x + 2y = 2 (-5)
5x - 3y = 4
- 5x - 10y = - 10
5x - 3y = 4 (+)
--------------------
- 13y = - 6 (-1)
13y = 6
Y = 6/13
X + 2y = 2
X + 2.6/13 = 2
X + 12/13 = 2
X = 2 - 12/13
X = (13.2 - 12)/13
X = (26-12)/13
X = 14/13
R.:
x = 14/13
Y = 6/13
___________
9)
2z = 4
z = 4/2
z = 2
W+z = 0
W +2= 0
W= - 2
3y +w - 3z = 2
3y +(-2) - 3.2 = 2
3y - 2 - 6 = 2
3y - 8 = 2
3y = 2+8
3y = 10
y = 10/3
x +y + w+ z = 8
X + 10/3 + (-2) + 2 = 8
x + 10/3 - 2 + 2 = 8
X + 10/3 = 8
X = 8 - 10/3
X = (3.8 - 10)/3
x = (24 - 10)/3
X = 14/3
14/3 + 10/3 + 2 - 2 = 24/3= 8
R.:
a) 8
________