1806 Strang a0 a1 a2 a3 2
2000-10-30
a4a6a5a6a7
a8a6a9a6a10a6a11a6a12
a7
1) M2 2-131 Holm 2-181 3-3665 tsh@math
2) M2 2-132 Dumitriu 2-333 3-7826 dumitriu@math
3) M3 2-131 Holm 2-181 3-3665 tsh@math
4) T10 2-132 Ardila 2-333 3-7826 fardila@math
5) T10 2-131 Czyz 2-342 3-7578 czyz@math
6) T11 2-131 Bauer 2-229 3-1589 bauer@math
7) T11 2-132 Ardila 2-333 3-7826 fardila@math
8) T12 2-132 Czyz 2-342 3-7578 czyz@math
9) T12 2-131 Bauer 2-229 3-1589 bauer@math
10) T1 2-132 Ingerman 2-372 3-4344 ingerman@math
11) T1 2-131 Nave 2-251 3-4097 nave@math
12) T2 2-132 Ingerman 2-372 3-4344 ingerman@math
13) T2 2-150 Nave 2-251 3-4097 nave@math
1
1 a13 36 a14a16a15a18a17 Q a19 4 3 a20a22a21a24a23a26a25 Q a27a6a28a22a29a24a30 q1; q2; q3
a31a6a32a6a33a6a34a6a35
(a) a36a6a37a6a38a6a39a6a40a6a41a6a42 Q a27a6a28a22a43a6a44a24a27a22a29a24a30 v a23a26a45a6a46a6a47 q1; q2; q3; v a48a6a49 Gram-
Schmidt
a33a6a34a6a50
a23a52a51a6a53a6a54a24a55a6a39
a31a6a32a6a33a6a34
a29a24a30 q4
a35
(b) a51a56a53 Q a27a56a57a58a43a56a44a60a59 QT a27a56a57a58a43a56a44a61a13a63a62a56a64
a7a52a65a60a66a56a67a58a68a60a69 (a)
a23a26a70a56a71a56a72a58a73a60a47
(b) a74a6a75a16a15
a35a26a76a6a77a6a78
a51a6a53 QTQ a59 QQT a27a6a57a22a43a6a44
a35
(c) a17 b = q1 + 2q2 + 3q3 + 4q4
a35a26a79
Qx=b a27a6a80a6a81a6a82a6a83a6a84 x
a35a26a85a6a79
a53 b a86 Q
a27a6a28a22a43a6a44a24a87a6a27a6a88a6a89 p
a35
2
2 a13 24 a14a16a15
(a) a90a6a80a6a81a6a82a6a83a6a91
a79a6a92a6a93
Ax=b a23a60a94a6a95
a92a6a93
Ax=b a19a6a46a6a96 (t,b)=(2,3),(3,5) a59
(4,K) a27a6a80a6a97a6a98a6a99a6a100a6a101a6a102a26a19a6a103a6a104a6a86 K a23a26a94a6a95
a92a6a93
Ax=b a105a6a106a6a107a6a84
a35
(b) a47a56a38a56a108a56a27 A,B,a86a56a109a58a110a60a111a56a112a56a113a56a23 x a19
a92a56a93
Ax=b a27a56a80a56a81a56a82a56a83a56a84a115a114a116a73 (a)
a117a6a118
a23a52a119a24a75a6a19a6a103 9K,s.t,x = 0 a19
a92a6a93
Ax=b a27a6a80a6a81a6a82a6a83a6a84a6a23
a85a6a120a22a121a24a122a6a35
3
3 a13 40 a14a16a15
(a) a17 A a19 4 4 a20a123a21a124a23a126a125a128a127a128a129a128a130 a14 a27a128a131a128a132a128a133 1 a23a126a49a128a28a128a134a128a27a128a131a128a105a128a109a123a110a124a135
a50
a114
(b) a136a6a84a6a137
a117
a109a22a110a24a138a6a39a6a88a6a89a6a20a22a21a24a27a6a49a6a28a6a134a6a139a6a19 0 a140 1
a35
(c)
a79a6a141a6a142
a20a22a21 A=
2
66
64
0 b 0 a
a 0 b 0
0 a 0 b
b 0 a 0
3
77
75 a27a6a49a6a28a6a134
a35
4
2000-10-30
a4a6a5a6a7
a8a6a9a6a10a6a11a6a12
a7
1) M2 2-131 Holm 2-181 3-3665 tsh@math
2) M2 2-132 Dumitriu 2-333 3-7826 dumitriu@math
3) M3 2-131 Holm 2-181 3-3665 tsh@math
4) T10 2-132 Ardila 2-333 3-7826 fardila@math
5) T10 2-131 Czyz 2-342 3-7578 czyz@math
6) T11 2-131 Bauer 2-229 3-1589 bauer@math
7) T11 2-132 Ardila 2-333 3-7826 fardila@math
8) T12 2-132 Czyz 2-342 3-7578 czyz@math
9) T12 2-131 Bauer 2-229 3-1589 bauer@math
10) T1 2-132 Ingerman 2-372 3-4344 ingerman@math
11) T1 2-131 Nave 2-251 3-4097 nave@math
12) T2 2-132 Ingerman 2-372 3-4344 ingerman@math
13) T2 2-150 Nave 2-251 3-4097 nave@math
1
1 a13 36 a14a16a15a18a17 Q a19 4 3 a20a22a21a24a23a26a25 Q a27a6a28a22a29a24a30 q1; q2; q3
a31a6a32a6a33a6a34a6a35
(a) a36a6a37a6a38a6a39a6a40a6a41a6a42 Q a27a6a28a22a43a6a44a24a27a22a29a24a30 v a23a26a45a6a46a6a47 q1; q2; q3; v a48a6a49 Gram-
Schmidt
a33a6a34a6a50
a23a52a51a6a53a6a54a24a55a6a39
a31a6a32a6a33a6a34
a29a24a30 q4
a35
(b) a51a56a53 Q a27a56a57a58a43a56a44a60a59 QT a27a56a57a58a43a56a44a61a13a63a62a56a64
a7a52a65a60a66a56a67a58a68a60a69 (a)
a23a26a70a56a71a56a72a58a73a60a47
(b) a74a6a75a16a15
a35a26a76a6a77a6a78
a51a6a53 QTQ a59 QQT a27a6a57a22a43a6a44
a35
(c) a17 b = q1 + 2q2 + 3q3 + 4q4
a35a26a79
Qx=b a27a6a80a6a81a6a82a6a83a6a84 x
a35a26a85a6a79
a53 b a86 Q
a27a6a28a22a43a6a44a24a87a6a27a6a88a6a89 p
a35
2
2 a13 24 a14a16a15
(a) a90a6a80a6a81a6a82a6a83a6a91
a79a6a92a6a93
Ax=b a23a60a94a6a95
a92a6a93
Ax=b a19a6a46a6a96 (t,b)=(2,3),(3,5) a59
(4,K) a27a6a80a6a97a6a98a6a99a6a100a6a101a6a102a26a19a6a103a6a104a6a86 K a23a26a94a6a95
a92a6a93
Ax=b a105a6a106a6a107a6a84
a35
(b) a47a56a38a56a108a56a27 A,B,a86a56a109a58a110a60a111a56a112a56a113a56a23 x a19
a92a56a93
Ax=b a27a56a80a56a81a56a82a56a83a56a84a115a114a116a73 (a)
a117a6a118
a23a52a119a24a75a6a19a6a103 9K,s.t,x = 0 a19
a92a6a93
Ax=b a27a6a80a6a81a6a82a6a83a6a84a6a23
a85a6a120a22a121a24a122a6a35
3
3 a13 40 a14a16a15
(a) a17 A a19 4 4 a20a123a21a124a23a126a125a128a127a128a129a128a130 a14 a27a128a131a128a132a128a133 1 a23a126a49a128a28a128a134a128a27a128a131a128a105a128a109a123a110a124a135
a50
a114
(b) a136a6a84a6a137
a117
a109a22a110a24a138a6a39a6a88a6a89a6a20a22a21a24a27a6a49a6a28a6a134a6a139a6a19 0 a140 1
a35
(c)
a79a6a141a6a142
a20a22a21 A=
2
66
64
0 b 0 a
a 0 b 0
0 a 0 b
b 0 a 0
3
77
75 a27a6a49a6a28a6a134
a35
4
