Equality of Matrices

Question 1: What is the Equality of Matrices?

Answer:

The equality of matrices is a concept of matrices that is defined by comparing two or more matrices that have the same dimensions and all the same corresponding elements.

Question 2: What are the conditions for the Equality of Matrices?

Answer:

The following are necessary conditions that are required for the equality for matrices A = [a_ij]_m×n and B = [b_ij]_p×q to be true:

Matrices A and B must have the same number of rows, i.e., m = p.
Matrices A and B must have the same number of columns, i.e., n = q.
The corresponding elements of matrices A and B must be equal, i.e., a_ij = b_ij for all i and j.

Question 3: How to prove that two matrices are equal?

Answer:

To prove that two matrices are equal, we have to prove that the order of the given matrices is equal, i.e., the same number of rows and columns, and also the corresponding elements are also equal.

Question 4: How can we solve the equality of matrices?

Answer:

Two equal matrices can be solved by comparing their corresponding elements. If there are any unknown variables, then solve them by equating them with the corresponding elements in the other matrix.

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.