What is Equality of Matrices?
When two or more matrices are equal, it is referred to as the equality of matrices. Matrices are considered to be equal if they have the same number of rows and columns, as well as the same number of elements. Equality of matrices does not hold for either of the previously mentioned conditions. The two matrices are said to be unequal if the order of the matrices is not equal or at least one pair of the corresponding elements is not equal. This concept is relevant for both- rectangular and square matrices.
Conditions for Equality Matrices
The equality of matrices is a concept of matrices that are defined by comparing two or more matrices that have the same dimensions and all the same corresponding elements. If “A = [aij]m×n” and “B = [bij]p×q” are two matrices, then the following are three requirements for matrix equality for matrices:
- The number of rows in matrices A and B is the same, i.e., m = p.
- The number of columns in matrices A and B is the same, i.e., n = q.
- For any i and j, the corresponding elements of A and B are equal, i.e., aij = bij.
Example:
Say . Find the values of a and z.
Because the order of the two matrices is equal, matrices are equal if and only if their corresponding elements are likewise equal.
Thus, comparing a and c to the corresponding elements of the other matrix, we have a = 69 and z = 420.
How to solve Equality of Matrices?
The equality of matrices is a mathematical concept where two or more matrices are equal when compared. Before learning the concept of equality of matrices, we need to know what a matrix is. A rectangle or square-shaped array of numbers or symbols organized in rows and columns to represent a mathematical object or one of its attributes is called a matrix in mathematics. The horizontal lines are said to be rows, while the vertical lines are said to be columns. For example, is a matrix with 3 rows and 3 columns. It can be called a “3 by 3” matrix and is a square matrix. On the other hand, is a “2 by 3” matrix and is a rectangular matrix.