Applications of Matrices and Determinants

A square matrix is called a matrix if its determinant is not equal to zero.

A square matrix is called matrix if its determinant is zero.

The matrix of of A is defined as the matrix obtained by replacing each element aij of A with the corresponding cofactor Aij

The matrix of A is defined as the transpose of the matrix of cofactors of A.

Let A be a square matrix of order X.If there exists a square matrix B of order n such that AB = BA = Iₓ , then the matrix B is called an of A.

If a square matrix has an inverse, then it is .

Let A be square matrix of order n.Then, A⁻¹ exists if and only if A is .

The determinant of a singular matrix is 0 and so a singular matrix has no .

If A and B are any two square matrices of order n , then adj(AB) = (adjB)(adjA).

A square matrix A is called if AAⁿ=AⁿA=I.

A is orthogonal if and only if A is .

is an art of communication between two people by keeping the information not known to others.

means the process of transformation of an information (plain form) into an unreadable form (coded form).

The matrix used for encryption is called matrix .

A matrix obtained by deleting some rows and some columns of A is called a of A.

The of a matrix A is defined as the order of a highest order non-vanishing minor of the matrix A.

An is defined as a matrix which is obtained from an identity matrix by applying only one elementary transformation.

Transforming a non-singular matrix A to the form In by applying elementary row operations, is called method.

A system of linear equations having at least one solution is said to be .

A system of linear equations having no solution is said to be .

Applications of Matrices and Determinants

Gap-fill exercise