Civil Engineering Reference
In-Depth Information
Example 2.2
Matrix multiplication
Multiply matrix [
A
] and [
B
] to get [
C
].
24
32
10
34
1 42324
232411
[]
=
[]
=
A
and
B
The product of a 4 × 2 matrix multiplied with a 2 × 6 matrix is a 4 × 6
matrix.
[] []
=
[]
AB C
42 26
×
×
46
×
24
32
10
34
10 20 12 22 8 2
7 81017814
142324
11 24 14 25 10 16
1 42324
232411
[[]
=
=
[]
=
AB
C
The first two elements are computed as follows:
=
()
+
()
=+=
=
()
+
()
=+ =
c
c
21 42 2810
24 43 812 0
11
12
2.3.4
MATRIX DETERMINANTS
A determinant is only defined for square matrices and can be easily
achieved through expansion by minors of a row or a column when dealing
with small matrices. A row expansion is as follows:
1
+
j
n
+
1
AaAaA
=
− +− +−
…
()
1
a A
…
()
1
a A
11
11
12
12
1
j
1
j
1
n
1
n
aa a
a
aa a
aa a
aa a
aa a
11
12
1
n
22
23
2
n
21
23
2
n
a
a
21
22
2
n
32
33
3
n
31
33
3
n
=
a
−
a
11
12
aa a
aa a
aa a
n
1
n
2
nm
n
2
n
3
nm
n
1
n
3
nm
aa a
aa a
21
22
21
,
n
−
31
32
31
,
n
−
1
+
j
n
+
1
++−
…
()
1
aA
+
…
()
−
1
a
1
j
1
j
1
n
aa a
n
1
n
2
nn
,
−
1
