Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Abstract Algebra: Theory and Applications
· Problem 20.8
Fields — Thomas Judson
Mathematics — Abstract Algebra · subspaces
Problem
Show that the set of all possible solutions
(
x
,
y
,
z
)
∈
R
3
(x, y, z) \in \mathbb{R}^3
(
x
,
y
,
z
)
∈
R
3
of the equations
A
x
+
B
y
+
C
z
=
0
Ax + By + Cz = 0
A
x
+
B
y
+
C
z
=
0
D
x
+
E
y
+
C
z
=
0
Dx + Ey + Cz = 0
D
x
+
E
y
+
C
z
=
0
form a subspace of
R
3
\mathbb{R}^3
R
3
.
Related theory
subspaces
Browse the problem library