determinant identities

If the rows and columns of a determinant are inter-changed, the value remains unaltered. If any two rows (columns) of a determinant are identical, its value of the determinant is zero. If any two rows (columns) of a determinant are interchan..

Summary - 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..

Solve the equation 4( x + 11) = 4 x + 16 and determine whether it has one solution, no solution, or is an identity. => One solution or No solution or Identity..

Solve the equation 2( x + 9) = 2 x + 6 and determine whether it has one solution, no solution or is an identity. => not enough information given or one solution or no solution or an identity..

Solve the equation 2( x + 2) = 2 x + 4 and determine whether it has one solution, no solution, or is an identity. => no solution or not enough information given or one solution or an identity..

Summary - 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..

In unisexual organisms, the chromosomes can be distinguished into autosomes and allosomes. Autosomes or somatic chromosomes carry genes which determine the somatic characteristics and do not have any influence on determining the sex of the organism. Allosomes are sex chromosomes..

In this type, the females have only one sex chromosome and hence represented as ZO. Females are heterogametic. Males carry two identical sex chromosomes designated ZZ. Males are homogametic. On fertilization by a Z-carrying sperm the Z-carrying ovum would develop into a male (ZZ) and on f..

In this type, the females carry two different types of sex chromosomes (ZW) and are heterogametic while males carry identical sex chromosomes (ZZ) and are homogametic. The ova will be of two types: Zcarrying and Wcarrying while all sperms will be only Z-carrying. The ovum will have a sex ..

The adjoint of a square matrix [aij] is defined as the transpose of the matrix [Aij] where Aij are the cofactors of the elements aij. Adjoint of A is denoted by adj A. Let A be a square matrix of order n. If there exists a matrix B of order n such that AB = BA = I, where I is the ..