MATRICES AND MATRIX OPERATIONS
(1)
When multiplying a 1
×
n
row matrix by an
n
×
1 column matrix, we simply multiply
the corresponding terms and sum them to get a 1
×
1 matrix, i.e.
r
1
r
2
r
3
...
r
n
c
1
c
2
c
3
.
.
.
c
n
=
r
1
c
1
+
r
2
c
2
+
r
3
c
3 +
...
+
r
n
c
n
(2)
There are 4 different matrix operations we may perform over 2 matrices:
•
Addition:
Add corresponding entries in the 2 matrices. Both matrices must be the
same dimension.
•
Subtraction:
Subtract corresponding entries in the 2 matrices. Both matrices must
be the same dimension.
•
Scalar multiplication:
Multiply ever entry in the matrix by the scalar.
•
Matrix multiplication:
Multiply each row matrix in the first matrix by the corre-
sponding column matrix in the second matrix.
We can only multiply an
m
×
n
matrix by an
n
×
p
matrix (i.e. the first matrix has the same number of columns as
rows of the second matrix) to obtain an
m
×
p
matrix.

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