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.
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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

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Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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