**Matrix | What is Matrix? **

A **matrix** is a rectangular array of
numbers arranged in horizontal and vertical lines and enclosed between round or
square brackets. Horizontal lines are called rows and vertical lines are called
columns of a matrix.

Some examples of matrix are given below:

Each member or number in the array is
called an element or an entry of the matrix. An element appearing in the i^{th}
row and j^{th} column of a marix is called its (i, j)^{th}
element or the (i, j)^{th} entry.

**Order of a Matrix**

The order or the size of the matrix is
given by the number of rows followed by the number of columns. If a matrix
contains m rows and n columns, then it is of order m × n, read as m by n.

**Matrix Notation**

The matrices are usually denoted by capital
letters such as A, B, C, ………etc. The elements are denoted by the corresponding
small letters along with two suffixes. The first suffix indicates the number of
row and latter one indicates the number of column in which the element appears.

a_{ij} is the element of a matrix A in the
i_{th} row and j_{th} column.

a_{23} is the element of a matrix A in the
2^{nd} row and 3^{rd} column.

Thus a matrix of order m × n may be written as

A = (a_{ij})_{m × n}

If A is a 3 × 3 matrix, then it may be written as

**Types of Matrices**

**1. ****Row Matrix: **

**2. ****Column Matrix: **

**3. ****Square Matrix:**

**4. ****Rectangular Matrix: **

**5. ****Zero Matrix or Null Matrix:
**

**6. ****Diagonal Matrix: **

**7. ****Scalar Matrix: **

**8. ****Unit Matrix or Identity
Matrix: **

**Equal Matrices**

Two matrices A and B are said to be equal matrices
if A and B are of same order i.e. number of rows in A = number of rows in B and
number of columns in A = number of columns in B, and their corresponding
elements are equal i.e. the entries of A and B in the same position are equal.
Otherwise, the matrices are said to be unequal.

If A and B are equal matrices, then we write A =
B. Otherwise, we write A ≠ B.

For example:

*Worked Out Examples*

*Worked Out Examples*

*Example 2: If a matrix has 6 elements, what are the possible orders
it can have?*

*Solution:*

*If a matrix has 6 elements, then it can have any one of the
following orders:*

*1 × 6, 6 × 1, 2 × 3 or 3 × 2.*

*Example 3: Construct a 2 × 2 matrix whose elements a _{ij}
are given by a_{ij} = i + j.*

*Example 4: Construct a 2 × 2 matrix A whose element a _{ij}
are given by a_{ij} = 3i + 2j.*

*You can comment your questions or problems regarding the matrix,
order of matrix and the types of matrices here.*

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