Category: Mathematics

Addition Theorem on Probability

For any two event A, B the Probability of A union B equals to probability of A added to probability of B minus probability of A intersection B. P (A∪B) = P(A) + P(B) – P(A∩B) Proof :- Suppose, the simple events in A∩B are γ1, …

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Random Experiment or Trail and Various Events of a Random Experiment

Random Experiment or Trail An experiment which satisfies the following conditions is called as a random experiment. It can be conducted several number of times under similar conditions. The list of all the outcomes of the experiment must be known. The result of the experiment is …

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What is an Elementary Matrix

Elementary Matrix In mathematics, an elementary matrix is nothing but a matrix obtained by performing only one elementary transformation. They can be denoted as follows: Elementary matrix obtained by interchanging i, jth rows of I is denoted by Eij. Elementary matrix obtained by multiplying ith row …

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System of Non-Homogeneous Linear Equations

Non-Homogeneous Linear Equations:- a1 x + b1 y + c1 z = d1a2 x + b2 y + c2 z = d2 a3 x + b3 y + c3 z = d3 is called a system of non-zero homogeneous linear equations. then it can be written …

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System of Homogeneous Linear Equations

Homogeneous Linear Equations:- a1 x + b1 y = 0a2 x + b2 y = 0 is called a system of homogeneous linear equations in x and y. Then the above system can be written as AX = 0 Definitions Coefficient Matrix :- In the system …

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