The order of a matrix or the size of a matrix is known as the number of rows or the number of columns which are present in that matrix.

The order of above matrix is 2 x 4. Because in the above matrix there are two rows and four columns.

The element which occurs in a₁₁  =  5

The element which occurs in  a₁₂  =  -2

The element which occurs in  a₁₃  =  7

The element which occurs in  a₁₄  =  9

The element which occurs in a₂₁  =  3

The element which occurs in a₂₂ = 1

The element which occurs in a₂₃  =  2

The element which occurs in a₂₄  =  -8

Minor of matrix :

Minor of a matrix may defined as follows.

Let |A|  =  |[a_ij]| be a determinant of order n.

The minor of an arbitrary element a_ij is the determinant obtained by deleting the i^th row and j^th column in which the element a_ij stands. The minor of a_ij by M_ij.

Examples of finding minor of a matrix

Cofactor of matrix :

The cofactor is a signed minor. The cofactor of a_ij is denoted by A_ij and is defined as A_ij = -1^(i+j) M_ij.

Examples of finding cofactor of matrix

Adjoint of matrix :

Let A = [a_ij] be a square matrix of order n. Let A_ij be a cofactor of a_ij. Then nth order matrix [A_ij]^T is called adjoint of A. It is denoted by adj A. In other words we can define adjoint of matrix as transpose of co factor matrix.

Examples of finding adjoint of matrix

Inverse of matrix :

If A is a non-singular matrix,there exists an inverse which is given by

Examples of finding inverse of matrix

Related Pages

• Types of matrices
• Equality of matrices
• Operation on matrices
• Algebraic properties of matrices
• Multiplication properties
• Minor of a matrix
• Practice questions of minor of matrix
• Adjoint of matrix
• Adjoint of matrix worksheets
• Determinant of matrix
• Inverse of a matrix
• Practice questions of inverse of matrix
• Inversion method
• Inversion method worksheets
• Cramer's Rule for 3 equations
• Cramer's Rule for 2 equations
• Solving 2 equations using Cramer's method
• Rank Method in Matrix
• Rank of a matrix
• Solving using rank method
• Linear dependence of vectors
• Linear dependence of vectors in rank method
• Characteristic Equation of matrix
• Characteristic vector of matrix
• Diagonalization of matrix
• Gauss elimination method
• Matrix calculator
• Matrix worksheets

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