18.5 Matrix Algebra 611
This is a good place to define a symmetric matrix. Asymmetric matrixis a square matrix
whose elements are symmetrical with respect to its principal diagonal. An example of a sym-
metric matrix follows.Example 18.2 Given the following matrices: , perform the
following operations: (a) [A]
T
? and (b) [B]
T
?(a) As explained earlier, the first, second, third,... , andmth rows of a matrix become the first,
second, third, ..., andmth column of the transpose matrix, respectively.(b) Similarly,
Determinant of a Matrix
Up to this point, we have defined essential matrix terminology and discussed basic matrix oper-
ations. In this section, we will define what is meant by adeterminant of a matrix. Let us con-
sider the solution to the following set of simultaneous equations:(18.14a)
a 21 x 1 a 22 x 2 b 2 (18.14b)
a 11 x 1 a 12 x 2 b 1
3 B 4
T
£47 1
62 3
23 4
§
3 A 4
T
£08 9
53 2
07 9
§
3 A 4 £
050
837
9 29
§ and 3 B 4 £
46 2
72 3
13 4
§
3 A 4 ≥
14 2 5
4 5 15 20
215 38
520 8 0
¥
5 U 6 e
7
4
9
6
12
u by 3 U 4
T
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