Civil Engineering Reference
In-Depth Information
Subtraction
:
246
793
651
124
652
430
122
141
221
[]
−
[]
=
AB
−
=
2.3.2
SCALAR MULTIPLICATION
Scalar multiplication consists of multiplying a matrix by a scalar.
When this occurs, every entry is multiplied by that scalar as seen in the
following:
aaa
a
ca
ca
ca
ca
11
12
13
1
m
11
12
13
1
m
aaa
a
ca
ca
ca
ca
21
22
23
2
m
21
22
23
2
m
[]
=
cA c
aaa
a
=
c
aaa a
ca
31
32
33
3
m
31
32
33
3
m
aaa
a
ca
ca
ca
ca
n
1
n
2
n
3
nm
n
1
n
2
n
3
nm
2.3.3
MATRIX MULTIPLICATION
Matrix multiplication proves a little more complicated than scalar
multiplication. In order for two matrices to be multiplied, the number
of columns in the first matrix must equal the number of rows in the
second matrix. The resulting product consists of the same number of
rows as the first matrix and the same number of columns as the second
matrix.
[] []
=
[]
×
AB C
nm mo
×
no
×
Each term of the product matrix (row
i
and column
j
) is obtained by
multiplying each term in row
i
of the first matrix by the term in row
j
of
the second matrix and then summing these products.
+
…
+
cabab
=
+
a b
ij
i
11
j
i
22
j
in nj
