Problems 31-40 refer to the partially completed table below of the 10 basic solutions to the e-system x 1 + x 2 + s 1 = 24 2 x 1 + x 2 + s 2 = 30 4 x 1 + x 2 + s 3 = 48 x 1 x 2 s 1 s 2 s 3 A 0 0 24 30 48 B 0 24 0 6 24 C 0 30 − 6 0 18 D 0 48 − 24 − 18 0 E 24 0 0 − 18 − 48 F 15 0 9 0 − 12 G 0 0 H 0 0 I 0 0 J 0 0 In the basic solution E , which variables are nonbasic?
Problems 31-40 refer to the partially completed table below of the 10 basic solutions to the e-system x 1 + x 2 + s 1 = 24 2 x 1 + x 2 + s 2 = 30 4 x 1 + x 2 + s 3 = 48 x 1 x 2 s 1 s 2 s 3 A 0 0 24 30 48 B 0 24 0 6 24 C 0 30 − 6 0 18 D 0 48 − 24 − 18 0 E 24 0 0 − 18 − 48 F 15 0 9 0 − 12 G 0 0 H 0 0 I 0 0 J 0 0 In the basic solution E , which variables are nonbasic?
Solution Summary: The author explains the non-basic variables of the e-system (E).
Problems 31-40 refer to the partially completed table below of the
10
basic solutions to the e-system
x
1
+
x
2
+
s
1
=
24
2
x
1
+
x
2
+
s
2
=
30
4
x
1
+
x
2
+
s
3
=
48
x
1
x
2
s
1
s
2
s
3
A
0
0
24
30
48
B
0
24
0
6
24
C
0
30
−
6
0
18
D
0
48
−
24
−
18
0
E
24
0
0
−
18
−
48
F
15
0
9
0
−
12
G
0
0
H
0
0
I
0
0
J
0
0
In the basic solution
E
, which variables are nonbasic?
Find the exact values of sin(2u), cos(2u), and tan(2u) given
2
COS u
where д < u < π.
2
(1) Let R be a field of real numbers and X=R³, X is a vector space over R, let
M={(a,b,c)/ a,b,cE R,a+b=3-c}, show that whether M is a hyperplane of X
or not (not by definition).
متکاری
Xn-XKE
11Xn-
Xmit
(2) Show that every converge sequence in a normed space is Cauchy sequence but
the converse need not to be true.
EK
2x7
(3) Write the definition of continuous map between two normed spaces and write
with prove the equivalent statement to definition.
(4) Let be a subset of a normed space X over a field F, show that A is bounded set iff
for any sequence in A and any sequence in F converge to zero the
sequence converge to zero in F.
އ
Establish the identity.
1 + cos u
1 - cos u
1 - cos u
1 + cos u
= 4 cot u csc u
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