Matrix

1. Definition of a Matrix
1. A matrix is an arrangement of numbers or variables in a rectangular form, enclosed by parentheses .
2. Each number or variable within a matrix is called an element of the matrix.
3. The horizontal rows in a matrix are called rows, and they are numbered from top to bottom as the 1st row, 2nd row, and so on. The vertical columns are called columns, and they are numbered from left to right as the 1st column, 2nd column, and so on.
   
   


2. Matrix
   A matrix with rows and columns is called an matrix. A matrix in which the number of rows is equal to the number of columns is called a square matrix, and an matrix is referred to as an -order square matrix.
   
   
   
   
   
   
3. The Element of a Matrix
1. Matrices are usually denoted by capital letters like , , , etc., while their elements are denoted by lowercase letters like , , , etc.
2. The element at the intersection of the -th row and -th column in matrix is called the element of matrix and is written as . Thus, matrix can be written as .


4. Condition for Two Matrices to be Equal
1. Two matrices and are said to have the same form if they have the same number of rows and columns.
2. Two matrices and are equal if they have the same form and each corresponding element is equal. This is denoted as .
   For example, if , , then:
3. If and , then .


5. If two matrices and are not equal, this is denoted as .