Matrix Operations
•
Since they are both 2 x 2, we can add them:
A+B=[;
~]+[~
~]=[::]
•
Or subtract
one from the other:
Matrix Operations
•
Matrix
Multiplication
To multiply
two matrices,
the
number
of columns
in the first must be the same as the
number
of rows in the second,
in which case they are
conformable
for multiplication.
•
A simple way to check the conformability
of two matrices
for multiplication
is to write down the dimensions
of the
operation,
for example
(n
x
k)
times
(k
x
t).
The inner
dimensions
must be equal.
•
The result has dimensions
equal to the outer values.
That
is, the result would have dimension
(n
x
t).
Example:
Matrix Multiplication
[
2 0~4 I 3]
MN=
~
~p
7
2
[
2.4+0.1
2·1+0·7
=
5·4+3·1
5·1+3·7
1·4+6·1
1·1+6·7
[
8 2 6]
=
23
26
21
10
43
15
2.3+0.2]
5·3+3·2
1·3+6·2
Matrix Operations
•
Scalar
Multiplication
To multiply
a matrix by a number

or in matrix terminology,
by a scalar 
is to multiply
every element
of that matrix by the given scalar.
•
Example:
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