MATRIX IS JUST ANOTHER NUMBER

Matrix is square or rectangular table of numbers arranged in rows and columns. It looks simple. But its potential is immense.
If matrix is just another kind of numbers like integers, fractions, what is 0,1,-1 and i in matrix-kind. We will find out.

First, we should learn matrix multiplication.
Multiplication of matrices is the important operation and it is highly useful. To multiply two matrices, number of rows of one matrix must be equal to the number columns of another matrix.

MULTIPLYING MATRIX A AND B

[a b * [e f = [ae +bg af +bh
c d] g h] ce +dg cf +dh]
A B = C

This is how you multiply order of two matrices.
Column elements in one matrix is multiplied by corresponding row elements in another matrix and summed up to get the new element.
Why we multiply this way?
Consider this set of equations.
4x +2y+z = 10
2x +3y+4z =25

[4 2 1 * [x = [10
2 3 4] y 25]
z]
If you multiply the matrices following the rules, you will get back the equations. That is matrix. Again, if we follow the rules of matrix multiplication, the matrix operators and matrix entities will hold good.

'0' is the null matrix as
0 = [0 0
0 0] order of 2, must be square
0 =[000
000
000] order of 3
this, we can understand

unit matrix = '1' = I = [1 0
0 1]
or [100
010
001]
I*1 must be 1. 1*0 =0; only this arrangement of matrix will meet these conditions.

-1 = [-1 0
0 -1]
It is also logical. -1*-1 must be +1.
If you multiply above matrix by itself, it will yield unit matrix.

What about i, the imaginary number
i = [o -1
1 0]
If you find i^2, it will be equal to -1. Hence the matrix for 'i' is correct.
A matrix can have any order. It can be rectangular. It can be 3 or more dimensional.

Operations of Matrix:
If two matrices have equal dimensions, each corresponding element in them can be added. Subtraction can be done in the same way. There is no division operation for matrices.
But 'inverse of matrix' can be found. The procedure is complicated one.

We can perform magic with matrix. For example in Artificial intelligence, face recognition software uses matrices.
--------------------------------------------------------------------------------------------------

Comments

Your heart -you do not know

Size and Location: The human heart is roughly the size of a clenched fist and is located slightly to the left of the center of the chest. Despite its relatively small size, the heart plays a crucial role in pumping blood throughout the entire body. Heartbeat Variability: The heart does not beat at a constant rate. The interval between heartbeats can vary, and this variability is considered a sign of a healthy heart. Factors such as breathing, emotions, and physical activity influence the heartbeat. Electrical Conduction: The heart's contractions are controlled by electrical impulses. The sinoatrial (SA) node, often called the "natural pacemaker," generates electrical signals that regulate the heartbeat and coordinate the pumping of blood. Blood Pumping Capacity: On average, the human heart pumps about 2,000 gallons (or 7,570 liters) of blood each day. Over a lifetime, this amounts to pumping enough blood to fill several Olympic-sized swimming pools. Heart Chambers and V...

THE WORK HORSE "="

One cannot think of a mathematical step without 'is equal to ' . It balances right hand side and left hand side. It aids simplification and manipulation of a mathematical expression. example: 2(A+B) = C 2A+2B = C 2A = C-2B A = C-2B/ 2 In an electronic calculator, the pressing of ' = " sign executes an asthmatic expression or simply calculates. In computer languages, it plays very important role. A = B When a computer looks at this expression, the value stored in the location named B is just transferred to the storage named A . After execution both A and B will have the same value an...

How does your smart phone detect motion, steps, rotation, and location?

How it works-1 An accelerometer in a smartphone is a microelectromechanical system (MEMS) device that measures acceleration and tilt. It works by detecting changes in motion by measuring the vibration or acceleration of the device. The accelerometer consists of a small mass suspended on a spring inside a sealed chamber. When the device is subjected to acceleration, the mass moves relative to the device, causing a change in capacitance that can be measured and processed by the smartphone's hardware. The accelerometer measures acceleration in three dimensions (x, y, and z) and provides data that the smartphone's software can use to determine the device's orientation, detect motion, and track changes in velocity and acceleration. The accelerometer is used for a variety of purposes in a smartphone, including screen rotation, motion tracking for games and fitness apps, and detecting the position of the device for navigation and location services. Additionally, it can be used t...

sciencecapsules

Search This Blog