GAAL
Pesquisas Acadêmicas: GAAL. Pesquise 862.000+ trabalhos acadêmicosPor: marianabp97 • 11/3/2015 • 1.683 Palavras (7 Páginas) • 179 Visualizações
1. (a) M11 = 7 • 4–(–1) • 1 = 29, M12 = 21, M13 = 27, M21 = –11, M22 = 13, M23 = –5, M31 = –19, M32 = –19, M33 = 19
(b) C11 = 29, C12 = –21, C13 = 27, C21 = 11, C22 = 13, C23 = 5, C31 = –19, C32 = 19, C33 = 19
2. (a)
(b)
(c)
(d)
MC 21 21 4 1 6 4 1 14 4 1 2 96; 72= − = − = −
MC 22 22 4 1 6 4 1 14 4 1 2 0;0 = = =
M
4 1 –6 4 1 14 4 1 2
C 2323 96; 96 = = − =
M
0 0 3 4 1 14 4 1 2
C 13 13 3 41 41 0;0 = = + ⋅ = =
103
3. (a)
(b) |A| = 1 • M11 – 6 • M21 – 3 • M23 = 152
(c) |A = 6 • M21 + 7 • M22 + 1 • M23 = 152
(d) |A| = 2 • M12 + 7 • M22 + 1 • M32 = 152
(e) |A| = –3 • M31 – 1 • M32 + 4 • M33 = 152
(f) |A| = 3 • M13 + 1 • M23 + 4 • M33 = 152
4. (a)
(b) From Exercise 3.(a), |A| = 152. Hence
5. Second column:
6. Second row:
A = − ⋅ −
+⋅ − = − + − =1 31 35 4 33 13 18 48 −66
A =⋅ − − = ⋅ − = −5 37 15 5 8 40
A− = − −1 29 152 11 152 19 152 21 152 13 152 1 / / / //99 152 27 152 5 152 19 152 / / / /
=
/// /// / 29 152 11 152 1 8 21 152 13 152 1 8 27 15 − − 225/1521/8
adj A
CC
() =
11 21 31
12 22 32
13 23 33
C CCC CCC
= − −
29 11 19 21 13 19 27 5 19
(see Exercise 1.(b.))
A =⋅ −
+⋅ − −
+⋅ −
1
71 14
2
61 34
3
67 331
29 42 81 152 =++=
104 Exercise Set 2.1
7. First column:
8. Second column: = –(k – 1)(2k – 20) + (k – 3)(k + 1) – 35_ – (k + 1)(4k – 10) = k3 – 8k2 – 10k + 95
9. Third column:
10. First row:
11.
12.
adj(A)= −
−−−
12 0 9 4 2 4 6 0 6 ;;;
/ ///AA = − = −− −6 2 0 3 2 2 3 1 3 2 3 1 0 1 1
adj(A)= −
−− −
355 345 223 ;; AA = − =
−− −
−−
−1
355 3 4 5 223
1
A =⋅ − −⋅4
3 3 1 0 2 4 2 3 4 6 2 3 2 4 2 3
1
3330 1 2243 9463 2243
000 =+=
A = − ⋅ − − ⋅ − 3 3 3 5 2 2 2 2 10 2 3 3 3 5 2 2 2 4 110 240=−
Ak
k
k
k
k
k ( ) ( ) ( ) = − − ⋅ + − ⋅ + −+1 24 5 3 15 7 1 ⋅⋅ +k 17 24
A
kk kk
kk kk
kk kk = ⋅ − ⋅ + ⋅ = 1 1 1 0 2 2 2 2 2 2
Exercise Set 2.1 105
13.
14.
15. (a)
(b) Same as (a).
(c) Gaussian elimination is significantly more efficient for finding inverses.
16.
x1 = 13/13 = 1, x2 = 26/13 = 2
AA 22 73 35 ;26= =
AA 11 32 51 ;13= − =
AA ,;= − = 72 31 b13 b= 3 5
A− =
−− −
−−
...