Addition of Matrices

Addition of Matrices

Concept from a Real-World Situation

Consider a manufacturer, Fatima, who owns two factories — one at location A and another at location B. Each factory produces sports shoes for boys and girls in three price categories: 1 (budget), 2 (mid-range), and 3 (premium). The production quantities from each factory can be arranged in a matrix, where rows represent price categories and columns represent gender (boys, girls).

Factory A's production matrix:

Factory B's production matrix:

If Fatima wants the total production of shoes in each price category for both genders, she adds the corresponding entries from the two matrices. The result is a new matrix:

This new matrix is called the sum of matrices $A$ and $B$. The operation is performed by adding the corresponding elements of the two matrices.

Formal Definition of Matrix Addition

Let $A = [a_{ij}]$ and $B = [b_{ij}]$ be two matrices of the same order, say $m \times n$. Then the sum $A + B$ is defined as a matrix $C = [c_{ij}]_{m \times n}$, where

for all values of $i$ (from 1 to $m$) and $j$ (from 1 to $n$). In other words, add each entry of the first matrix to the corresponding entry of the second, keeping the same position.

Binary Operation on Matrices …