18.06
a0 a1
1 a2 a3
2000 a4 3 a5 1 a6
a7 1.
(a) a8a10a9a10a11a13a12a15a14a13a16a15a17a10a18a10a18a10a19a10a20a10a21a23a22a13a24 3 a18a10a19a10a25 [0; 0; 0; 1] a21a23a9a10a26a10a27a10a28 0 =
1 a21a30a29a32a31a34a33a34a35a34a36a34a37a34a38
(b) a39a32a40a34a41a34a42a34a21a23a43a34a44a34a33a34a35 Ax = b a45a34a37a34a21 b a46a34a47a34a48a34a49 b1 + b2 = b3 a38
(c) a50 A a41a34a51a34a21a23a22 Ax = b a52a34a45a34a37a34a38
a7 2.
(a)
A = LU =
2
64 1 0 01 1 0
0 1 1
3
75
2
64 2 2 10 3 1
0 0 3
3
75
(b) a53 (a) a54a56a55 U a41a58a57a56a59a58a60a56a9a62a61a62a63a62a64a62a65a62a66a62a67a62a68a62a64a62a38a70a69 Aa42a62a67a62a68a62a64a62a66a62a9a62a64a58a71a62a72
a55a62a63a62a73a62a74a62a75 (2; 2; 0); (2; 5; 3); (1; 0; 2) a38a76a29a56a25a62a77a62a25 3a21a78a22a62a64a58a71a62a72a56a66a58a79a56a80 R3 a71a62a72a56a38
a29a32a31a34a41a34a81 R3 a55a34a82a34a83a34a74 (1; 0; 0); (0; 1; 0); (0; 0; 1) a84a34a25a34a64a85a71a34a72a32a55a85a86a32a87a34a63a34a73a34a74a34a38a23a88
a89a32a90
a21 R3 a54a32a91a34a92a34a93a34a80a34a94a34a95a34a96a34a97a34a55a85a98a32a99a34a65a34a66a34a64a85a71a34a72a32a55a34a63a34a73a34a74a34a38
(c)A a55a34a77a34a25 3 a21a30a29a32a25a34a45 3 a80a34a67a34a68a34a38
a7 3.
(a) a100a34a66a34a63a34a80 LU a101a34a37a34a38 U a66 A a55a34a102a34a103a34a103a34a104a34a38a30a29a32a31a34a41a34a59a34a105a34a106a34a45 3 a80a34a67a34a68a34a21
a29a32a31 A a55a34a77a34a66 3 a38
(b)N(A)a55a107a63a107a73a107a74a107a66a108a69a109a9a107a110a107a37a107a73a107a111a107a38a112a100a107a113a62a110a107a37a62a66a107a75 ( 1; 2; 1; 0; 0); ( 1; 1; 0; 1; 1) a38
1
(c) a114a34a115a34a63a34a80a34a110a34a37 ( 30; 15; 0; 10; 0) a21a23a22a34a9a34a116a34a37a34a25
2
66
66
64
30
15
0
10
0
3
77
77
75 + x3
2
66
66
64
1
2
1
0
0
3
77
77
75 + x5
2
66
66
64
1
1
0
1
1
3
77
77
75
a7 4.
(a) a63a34a73a34a74a34a66
"
1 0
0 0
#;
"
0 1
0 0
#;
"
0 0
1 0
#;
"
0 0
0 1
#
a38
(b) a69 A a55a34a117a34a118a34a73a34a111a34a55a34a119a85a71a34a72a32a66a34a63a34a80a34a120 A a121a34a122a34a120 B a55a34a119a85a71a34a72a32a38
(c) a8a34a21a23a50a34a63a34a80a34a119a85a71a34a72 V a123a32a120 A a124 B a21a23a22a34a9a34a120a34a45 A B = I a38
(d) a125a34a126a34a124 (b) a26a85a39a32a38
a7 5.
a69a32a127a85a128a32a122a85a39a32a55a34a129a85a130a32a33a34a131a34a38a70a9a85a54a32a132a34a63a34a66a34a75a70a50 A2 = 0 a21a70a22 A2 a122a34a41a34a51a34a21a133a29a32a31 A
a122a34a41a34a51a34a38a30a29a32a25a34a41a34a51a34a14a85a16a32a55a34a134a34a41a34a51a34a21a23a135a85a136a32a66a34a137 A a41a34a51a34a21 A2 a41a34a51a34a38
2