Addition Theorem on Probability
MathematicsFor 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 […]
Mathematics
Random Experiment or Trail and Various Events of a Random Experiment
MathematicsRandom 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.
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What is an Elementary Matrix
MathematicsElementary 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
System of Non-Homogeneous Linear Equations
Mathematics
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
System of Homogeneous Linear Equations
MathematicsHomogeneous 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