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Kunze Linear Algebra
· Problem 2.2.4
Vector Spaces
Mathematics — Methods · spanning-set-for-subspace
Problem
Let
W
W
W
be the set of all
(
x
1
,
x
2
,
x
3
,
x
4
,
x
5
)
(x_1, x_2, x_3, x_4, x_5)
(
x
1
,
x
2
,
x
3
,
x
4
,
x
5
)
in
R
5
R^5
R
5
which satisfy
2
x
1
−
x
2
+
4
3
x
3
−
x
4
=
0
2x_1 - x_2 + \tfrac{4}{3}x_3 - x_4 = 0
2
x
1
−
x
2
+
3
4
x
3
−
x
4
=
0
x
1
+
2
3
x
3
−
x
5
=
0
x_1 + \tfrac{2}{3}x_3 - x_5 = 0
x
1
+
3
2
x
3
−
x
5
=
0
9
x
1
−
3
x
2
+
6
x
3
−
3
x
4
−
3
x
5
=
0.
9x_1 - 3x_2 + 6x_3 - 3x_4 - 3x_5 = 0.
9
x
1
−
3
x
2
+
6
x
3
−
3
x
4
−
3
x
5
=
0.
Find a finite set of vectors which spans
W
W
W
.
Related theory
Trees Spanning Trees And Minimum Spanning Trees
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