Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Kunze Linear Algebra
· Problem 2.1.7
Vector Spaces
Mathematics — Methods · vector-space-axioms
Problem
Let
V
V
V
be the set of pairs
(
x
,
y
)
(x, y)
(
x
,
y
)
of real numbers and let
F
F
F
be the field of real numbers. Define
(
x
,
y
)
+
(
x
1
,
y
1
)
=
(
x
+
x
1
,
0
)
(x, y) + (x_1, y_1) = (x + x_1, 0)
(
x
,
y
)
+
(
x
1
,
y
1
)
=
(
x
+
x
1
,
0
)
c
(
x
,
y
)
=
(
c
x
,
0
)
.
c(x, y) = (cx, 0).
c
(
x
,
y
)
=
(
c
x
,
0
)
.
Is
V
V
V
, with these operations, a vector space?
Related theory
Vector Spaces Definition And Axioms
Browse the problem library