We proceed the same way to obtain the second row of
In other words, row 2 of
times column 1 of
row 2 of
times column 2 of
row 2 of
times column 3 of
When complete, the product matrix will be
Properties of matrix multiplication
For the matrices
and
the following properties hold.
Matrix multiplication is associative:
Matrix multiplication is distributive:
Note that matrix multiplication is not commutative.
Multiplying two matrices
Multiply matrix
and matrix
First, we check the dimensions of the matrices. Matrix
has dimensions
and matrix
has dimensions
The inner dimensions are the same so we can perform the multiplication. The product will have the dimensions
As the dimensions of
are
and the dimensions of
are
these matrices can be multiplied together because the number of columns in
matches the number of rows in
The resulting product will be a
matrix, the number of rows in
by the number of columns in
The dimensions of
are
and the dimensions of
are
The inner dimensions match so the product is defined and will be a
matrix.
Yes, consider a matrix A with dimension
and matrix B with dimension
For the product AB the inner dimensions are 4 and the product is defined, but for the product BA the inner dimensions are 2 and 3 so the product is undefined.
Using matrices in real-world problems
Let’s return to the problem presented at the opening of this section. We have
[link] , representing the equipment needs of two soccer teams.
Wildcats
Mud Cats
Goals
6
10
Balls
30
24
Jerseys
14
20
We are also given the prices of the equipment, as shown in
[link] .
Goal
$300
Ball
$10
Jersey
$30
We will convert the data to matrices. Thus, the equipment need matrix is written as
The cost matrix is written as
We perform matrix multiplication to obtain costs for the equipment.
The total cost for equipment for the Wildcats is $2,520, and the total cost for equipment for the Mud Cats is $3,840.
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life