A matrix is a collection of numbers ordered by rows and columns. It is customary to enclose the elements of a matrix in parentheses, brackets, or braces. For example, the following is a matrix:

This matrix has two rows and three columns, so it is referred to as a “2 by 3” matrix. The elements of a matrix are numbered in the following way.

That is, the first subscript in a matrix refers to the row and the second subscript refers to the column. It is important to remember this convention when matrix algebra is performed.

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