Question

Can we add matrices of a different order?

Answer 1

Hint: Matrix addition does not follow the rules of arithmetic addition. Arithmetically any number can be added to any other number. However, in matrix addition, we need a few conditions to be satisfied. If the order of the matrix is not the same then it is not possible to add them.

Complete step by step Solution:
 Before going into the addition of the matrix, let us first know what matrices are. In mathematics, a matrix is a blockish array of figures, expressions, or symbols, arranged in rows and columns. Horizontal rows are denoted by $m$ whereas the vertical columns are denoted by $n$. Therefore, a matrix $\left( {m \times n} \right)$ has $m$ and $n$ figures of rows and columns independently. We also know about different types of matrices such as square matrix, row matrix, null matrix, slant matrix, scalar matrix, identity matrix, slant matrix, triangular matrix, etc. Now, let us now concentrate on how to perform introductory operations on matrices similar to matrix addition and deduction with exemplifications.

The addition of a matrix is the basic operation performed for the addition of 2 or more matrices. Matrix operation is feasible on the condition that the order of the given matrices should be the same. By order, we tend to mean that the number of rows and columns of the given matrices is the same. Hence, we will add the corresponding terms of the matrices. However, if the order is completely different then matrix operation isn't attainable.

Let us consider two matrices, $A = {\left[ {{a_{ij}}} \right]_{m \times n}}$ and $B = {\left[ {{b_{ij}}} \right]_{m \times n}}$ of the order $\left( {m \times n} \right)$ , then the addition of A and B is given by:
 $A + B = {\left[ {{a_{ij}}} \right]_{m \times n}} + {\left[ {{b_{ij}}} \right]_{m \times n}}$
 $A + B = {\left[ {{a_{ij}} + {b_{ij}}} \right]_{m \times n}}$ which is possible since both the matrices have same order.

There are essentially 2 criteria that outline the concept addition of matrices.
They are as follows:
1. Think about 2 matrices A & B. These matrices will be added if (if and solely if) their order is the same i.e., the 2 matrices have an equal number of rows and columns.
2. The addition of 2 or more matrices is not outlined for matrices of a different order.
Hence, we get that if the order of the matrices is not the same then it is not possible to add them.


Note:We should not confuse the conditions of addition and multiplication of matrices. It is not compulsory for matrices to have the same order to multiply them. Rather, the multiplication of matrices has its own set of rules. Also, the condition for the subtraction of 2 or more matrices is the same as that of their addition.