May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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12-18 Discrete Mathematical Structures
We have been able to obtain a zero vector
xxxx
43
21
242−−−
and hence the vectors
xxxx
12
34
,,,and are linearly dependent.
Thus, we have
−
−−
−
+
+
+
−12 3
214
113
82 4
2
8
12 3
032
036
01
21
31
41
RR
RR
RR
∼
8820
6
123
032
004
008
2
32
42
4
−
−
−
−
RR
RR
RR
∼
33
123
032
004
000
∼
−
12.5.3 Echelon form of a Matrix
A matrix is said to be in echelon form if
1. all the non-zero rows, if any, precede zero rows;
2. number of zeros preceding the first non-zero element in a row is greater than the number
of such zeros in the preceding rows.
Rank of a Matrix: The number of non-zeros in the echelon form is defined as the rank of a
matrix. This is the number of linearly independent rows.
Example 1 Determine whether ...
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