Then
M349 Hw10 (S. Zhang)
1
QT AQ = D =
0. 5.5: 28-30,36-38, 42-45, 51-57, 61-64, 67-68, 73-74, 79-80,
88-92
1. (5.5:38)
Find an orthgonal transformation x = Qy so
that the quadratic form has no cross-product terms:
3
3
Let
x = Qy
f (x) = x2 + x2 + 3x2 4
M349 Hw11 (S. Zhang)
(b)
0. 7.2: 1-4, 9-12, 15, 22-23, 28-29, 35-38, 41,43-44
1. (7.2:22,28)
Compute A
and y with x 1 = 1 and y
and Ay
= A
and
=1
1
for A =
2
1
A = A A =
A . Find vectors x
so that Ax 1 = A 1
5
.
1
A
1
= max abs col sum = maxcfw_1 + | 2|,
M349 Study Guide for E 1 (S. Zhang)
90% of the exam is similar to the guide.
1. (2.2:12)
So
3s
s
x=
1 + 2t
t
0
3
0
0
1
0
= + s + t .
2
0
1
1
0
0
Find (1) REF, (2) RREF
A=
2
3
4
6
2
2
6
.
6
ans: We do 3 types of row operations on the matrix.
(1)
2
3
R2 +(
T
T
0
T
1
M349 Hw5 (S. Zhang)
E
0. 3.6: 1-2, 20-25, 36-39
1
0
0
0
1. (3.6:24)
Find the standard matrix of the linear transformation of R2 R2 : Reection in the line y = x
[0 1] stays.
Projection of [1 0] to [0 0].
ans:
T
T
y=x
0
T
d
1d
EE
T
d
d
E
s
1
0
A2
M349 H2 Solution (S. Zhang)
0. 2.4: 17-21, a1
1. (2.4:18)
(a) Set up and solve a system to nd the possible ows in the network.
1
1
0
0
0
0
1
R2 R1 0
0
0
0
1
R3 +R2
0
0
0
1
R4 +R3
0
0
1
R5 +R4
0
1
R6 R5
(b) Is it possible for f1 = 100 and f6 = 150? (an