definition of singular matrix

A square matrix A is said to be singular if |A| = ..

A square matrix A is said to be non-singular if its determinant value is non-zero. i.e.,..

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 o..

In other words, a square matrix A is invertible if and only if A is a non-singular matrix. (c) If A and B are invertible square matrices, then (AB) - 1 = B - 1 A - 1 (d) If A and B are two non-singular square matrices of the same order, then AB and..

They are spherical in shape. They can be further distinguished into Monococcus (occur singly) Diplococcus (occur in pairs) Tetracoccus (occur in groups of four) Streptococcus (occur in the form of a filament) and Staphylococcus (occur in the form of sheets). fig. 8.1 - Types of..

A matrix of order m x n whose elements are all 0 is called a null matrix (or zero matrix) of order m x n. It is usually denoted by O or more clearly [O] m , n..

It is a rectangular array of numbers, arranged in rows and columns. The number of rows (say m) and the number of columns (say n) determine the order of the matrix. It is written as m x n (to be read as m by n). The plural of matrix is matrices. Matrix is usually denot..

A rectangular array of entries is called a Matrix. The entries may be real, complex or functions. The entries are also called as the elements of the matrix. The rectangular array of entries are enclosed in an ordinary bracket or in square bracket. Matrices are denoted by capital..

A scalar matrix is a diagonal matrix in which all the diagonal elements are equa..

A matrix having only one row is called a row-matrix. For example: A[1 3 2 -2] is a row matrix of order 1 x..