field theory math

In this chapter, we have seen how arranging numbers in orderly rows and columns under the guise of Matrices and Determinants, has helped to solve linear equations or find the area of a triangle. There are in fact other much wider applications in Science and Engineering and other fieldsh..

Conclusion - We have seen the application of matrices and determinants in solving system of linear equation with three unknown variables. Matrices and determinants are also widely used in solving large system of linear equation. Some of these methods are Gauss-elimination method, Gauss-Jordan metho..

Introduction - The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematic..

Mathematical Induction..

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Principle of Mathematical Induction - If P(n) is a statement (n N); such that: P(1) is true and truth of P(k) implies the truth of P(k+1), then by the principle of mathematical induction (P.M.I.), the statement P(n) is true for n ..

If P(n) is a statement (n N); such that: P(1) is true and truth of P(k) implies the truth of P(k+1), then by the principle of mathematical induction (P.M.I.), the statement P(n) is true for n ..

Introduction - The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematic..

For any natural number n, prove tha..

A statement P(n) is true for all n N if (i) P(1) is true (ii) P(r) is true implies P(r+1) is tru..