what is matrix | Definition , Types And its Examples |

Matrix

A matrix is a two dimensional array of numbers having a fixed number of rows and columns and containing a number at the intersection of each row and each column . A matrix is usually delimited by square brackets.

[2  3 5]

Vectors

If a matrix has only one row only one column it is called a vector.

👉 A matrix having only one row is called a row vector.

The matrix is (1*3) row vector, because it has only one row.

👉 A matrix having only one column is called column vector.

B=2

     3

The matrixes (2*1) column vector because it has only one column.

 

Row Matrix

A matrix is said to be a row matrix if it has only one row.

for Example:

[1 2 3 4 5]

Column Matrix

A matrix is said to be a column matrix if it  has only one column.

For Example:

(1

2

3)

Rectangular Matrix:

A matrix is said to be a rectangular if the number of rows is not equal to the number of column.

Square Matrix:

A matrix is said to be square if the number of rows is not equal to the number of column.

A square matrix is matrix having squaing number of rows and colums.

For Example

A=(B)

B=  1  3            2   0  -3

      -5  4            1 -4   5

                         0  2    6

Diagonal Matrix:

A square matrix is said to be diagonal if at least one element of principal diagonal is nono-zero and all the other elements are zero.

scaler Matrix:

A diagonal matrix is said to be scalar if all of its diagonal elements are the same.

Identity  or Unit Matrix:

A diagonal matrix is said to be identity  if all of its diagonal elements are equal one , denoted by I.

Triangular Matrix:

A square matrix is said to be triangular if all of its elements above the principal diagonal are zero ( lower triangular matrix) or all of its elements below the principal diagonal are zero ( upper triangular matrix).

Null or Zero Matrix:

A matrix is said to be a null or zero if all of its elements are equal to zero . It is denoted by O.

Transpose of a Matrix:

suppose A is  a given matrix , then the matrix obtained by interchanging its rows into columns is called the transpose of A . it is denoted by At.

Algebra of Matrix:

The algebra of matrixes includes

1. Addition of matrixes 
2. Subtraction of matrixes
3. multiplication of matrix by scalar
4.Multiplication of matrixes

Addition of Matrices

two matrixes A and B can be added only if the order of matrix A is equal to the order of matrix B.

then, addition (A+B) of matrices A and B can be obtained by adding the corresponding elements A and B.

The order of (A+B ) is the same as the order of A the order Of B.

Subtraction Matrices

subtraction of two matrixes is similar to the addition of two matrices.Two matrices A and B are said to be conformable to subtraction A-B if both A and B have the same order. Subtraction can be done by taking the differences of the corresponding elements of matrices A and B . The order of A-B is the same as the order od A and Order B.

Multiplication of a Matrix by Scalar

Let A be any given matrix and let K be any real number (scalar ), then multiplication KA of the matrix A with the real number K is obtained by multiplying each element of the  matrix A by K.

 Multiplication of Matrix

Let A and B be any two given matrices , then the multiplication AB can be possible only if the number of columns of matrix A is equal to the  number of rows of matrix B. then multiplication AB can be obtained by the following method.

The element (1,1) position of AB is obtained by adding the products of the corresponding elements of the 1st row od A and the 1st column of B . Similarly the element (1,2) position of Ab is obtained by adding the products of the corresponding element of the 2nd row of A and 2nd column of B.