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How are matrix entries identified with row and column subscripts?

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vector parallelogram for addition and subtraction — linear algebra One method of adding and subtracting vectors is to place their tails together and then supply two more sides to form a parallelogram. The vector from their tails to the opposite corner of the parallelogram is equal to the sum of the original vectors. The vector between their heads (starting from the vector being subtracted) is equal to their difference.

In linear algebra, a matrix is typically denoted by a capital letter, while its individual elements—also called entries—are identified using the corresponding lowercase letter accompanied by a double subscript.1

The notation $a_{i j}$ represents the element located in the $i$ th row and the $j$ th column of a matrix $A$ . For example, in a matrix, the first subscript $i$ indicates the row position, and the second subscript $j$ indicates the column position. This systematic indexing allows for the precise identification and manipulation of every value within the rectangular array.1