The solution of systems of linear equations. Many issues related to systems of linear equations can be addressed by introducing a new concept, the matrix. Matrix theory plays a fundamental role in quite a few mathematical and statistical methods that are relevant for management.
We have introduced vectors as one-dimensional arrangement of numbers. A matrix is, in a sense, a generalization of vectors to two dimensions. Here are two examples of matrices:
In the following, we will denote matrices by boldface, uppercase letters. A matrix is characterized by the number of rows and the number of columns. Matrix A consists of three rows and three columns, whereas matrix B consists of two rows and four columns. Generally speaking, a matrix with m rows and n columns belongs to a space of matrices denoted by 
. In the two examples above, 
and 
. When m = n, as in the case of matrix A, we speak of a square matrix.
It is easy to see that vectors are just a special case of a matrix. A column vector belongs to space 
and a row vector is an element of 
.
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