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#INVERSE MATRIX

#IDENTITY MATRIX

#MATRIX ADDITION AND SUBSTRACTION

#MULTIPLICATION

#DETERMINANT OF A MATRIX

#CONTINUITY OF DETERMINANT

#MINOR AND COFACTOR

#ROW OF ECHELON

#CRAMER RULE

#GAUSS JOURDAN ELIMINATION METHOD

#SOLVING LINEAR EQUATION

There are different types ofmatriceslike rectangular matrix, null matrix, square matrix, diagonal matrix etc. This post covers overview of different types of matrices.

(1) Row Matrix:Row matrix is a type of matrix which has just one row. It can have multiple columns but there is just a single row present in a row matrix. Example of row matrix can be given as

A=[321] which has just one row but has three columns.

We can mathematically define row matrix as:

Matrix of the form A=[aij]1×nwhere 1 represents just a single row and n represents number of columns.

(2) Column Matrix:Column matrix is a type of matrix which has just one column. It can have multiple rows but there is just one column present in a column matrix. Example of column matrix can be given as:

A=⎡⎣15−2⎤⎦  which has just one column but has three rows.

We can mathematically define column matrix as:

Matrix of the form A=[aij]m×1 where m represents number of rows and 1 represents just a single column.

(3) Null Matrix:Null matrix is a type of matrix which has all elements equal to zero. Example of null matrix can be given as  A=[0000]. We can also mathematically define null matrix as:

A=[aij]m×nwhere aij=0for all i,j.

(4) Rectangular Matrix:Rectangular matrix is a type of matrix which has unequal number of rows and columns. Example of rectangular matrix can be given as

A=⎡⎣321−163⎤⎦, where we have unequal number of rows and columns in a matrix. Number of columns is 2 and number of rows is 3.

We can mathematically define rectangular matrix as matrix of the form A=[aij]m×nwherem≠n.

(5) Square Matrix: Square Matrixis a type ofmatrixwhich has equal number ofrowsandcolumns.Example of square matrix can be given as

A=⎡⎣−23−1056003⎤⎦, where we have equal number of rows and columns equal to 3.

We can define square matrix mathematically as matrix of the form A=[aij]m×nwherem=n.

(6) Diagonal Matrix:It is type of square matrix which has all the non-diagonal elements equal to zero. For example, matrix A=⎡⎣300050003⎤⎦is a diagonal matrix.

We can mathematically define diagonal matrix as a matrix of the form A=[aij]n×n, where aij=0wheni≠j.

(7) Identity Matrix:It is a type of square matrix which has all the main diagonal elements equal to 1 and all the non-diagonal elements equal to 0. It is also called unit matrix.

Example of unit matrix can be given as  A=⎡⎣100010001⎤⎦

We can mathematically define identity matrix as a matrix of the form A=[aij]n×n, where

aij=0for i≠jand aij=1for i=j.

(8) Scalar Matrix:It is a square matrix in which all the elements except those on the leading diagonal are zeros. For example,A=⎡⎣−200050003⎤⎦is an example of scalar matrix.

We can mathematically define scalar matrix as matrix of the form: A=[aij]n×n, where

aij=0for i≠jand aij=kfor i=j, where k is any scalar.

(9) Upper Triangular Matrix:It is a type of square matrix whose all elements below main diagonal are equal to 0. For example,A=⎡⎣−200350163⎤⎦is an example of upper triangular matrix.

We can mathematically define upper triangular matrix as matrix of the form:

A=[aij]n×nwhere aij=0for i>j.

(10) Lower Triangular Matrix:It is a type of square matrix whose all elements above main diagonal are equal to 0. For example.A=⎡⎣−23−1056003⎤⎦is an example of lower triangular matrix.

We can mathematically define lower triangular matrix as matrix of the form:

A=[aij]n×nwhere aij=0for j>i.