May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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Vector Spaces 12-17
23
34
0
41
21
xx
xx−+
()
+=
29340
41
21
xxxx
−−+=
23
50
421
xxx
−−=
(iii)
From relation (i),
xxx
123
,,are linearly dependent and from relation (iii)
xxx
124
,,are linearly
dependent. The vectors
xx
12
and
are linearly independent as
cx cx cc
12 12
12
00+=⇒==
.
Therefore, the given vectors are linearly dependent in R
4
.
12.5.2 Method for Testing Linear Dependence of Vectors
To test the linear dependence of n vectors
xx x
n12
,,..., ,
we write them as row vectors and add
such multiples of one vector to the remaining vectors so that the resulting vectors have their first
component zero. This gives (n - 1) new vectors all having their first component zero. Choosing
one of these new vectors, add its suitable multiples to others ...
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