polygon with unknown number of sides

>Now consider the system of linear equations with three variable Let the determinant of the coefficients be denoted by D i.e., Multiplying both sides by x, we have Adding y times column 2 and z times column 3 to column (1), we have Similarity it can be shown that, a..

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-Jo..

To find the logarithm of a Complex number - Let z= x + iy be a complex number. Taking log on both sides..

Matrix multiplication is not commutative in general. Matrix multiplication is associative i.e., (AB)C = A(BC), whenever both sides are defined. Matrix multiplication is distributive over matrix addition i.e., (i) A(B + C) = AB + BC (ii) (A + B)C = AB + AC whenever both sid..

(x 1 + x 2 ) + i (y 1 + y 2 ), i.e., z 1 + z 2 . The absolute values of z 1 , z 2 and z 1 + z 2 are geometrically given by We know that the sum of any two sides of a triangle is greater than the third. Hence, in D ORP, we have with the equality holding only when O, P, Q are ly..

If a:b=c:d, then a+b:b=c+d:d Adding 1 to both sides, we get ..

a:b::c:d Multiplying both sides by 2/3, we get Applying componendo and dividendo, 2a+3b:2a-3b=2c+3d:2c-3..

When 'n' is a fraction. where 'p' is any positive integer and 'q' is any integer. From Part I, Now taking q t h root of both sides, Hence the theor..

By componendo and dividendo, we get Squaring both sides, By componendo and dividendo, we get x(b 2 +1)=2ab ..

A matrix is defined as a rectangular array of elements. If the arrangement has m rows and n columns, then the matrix is of order mxn (read as m by n). A matrix is enclosed by a pair of parameters such as ( ) or [ ]. It is denoted by a capital letter. Two matrices are said to be comparable if t..