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In the realm of mathematics, particularly within the study of linear algebra, matrices are fundamental components that behave like a container for numbers, symbols, or expressions arranged in rows and columns. Picture a spreadsheet or a chessboard – these are everyday examples that share a grid-like structure similar to matrices. The entire arrangement forms a rectangular array, and each individual piece of data in a matrix is known as an entry or element.

Matrices are incredibly versatile and can represent systems of linear equations, perform linear transformations, and manage data in fields such as computer science, physics, and engineering. A matrix is usually denoted by a capital letter and can be identified by its dimensions; these are given by the number of rows followed by the number of columns, written in the format 'm x n'. In our case, the matrix B is written in the form of a 1x2 matrix, indicating that it consists of one row and two columns.

Zooming into the details, every position in a matrix is significant and holds value, quite literally. Matrix entries are the individual components of a matrix, found at the intersection of rows and columns. They are often denoted as 'a_{ij}' where 'i' and 'j' are the row and column indices, respectively. For matrices used in mathematical computations or representing real-world data, these entries could range from simple numerical values to more complex expressions.

To locate an entry, you've to count across the rows and down the columns, akin to following an address to a particular cell in a spreadsheet. In practice, these matrix entries are the building blocks for further operations such as addition, multiplication, and determining properties like the determinant or the inverse of a matrix. For example, in matrix B, the entry b_{12} corresponds to the element in the first row (i = 1) and second column (j = 2), which is the number 55 in this particular discussion.

Linear algebra serves as a powerful branch of mathematics that is central to understanding and working with matrices. It's all about vector spaces and the linear mappings that connect them. Often considered the language of applied mathematics and engineering, it lays the groundwork for concepts like vectors, matrix multiplication, determinants, and eigenvalues—all tools that play crucial roles in various mathematical and real-world applications.

In linear algebra, understanding the size or dimensions of a matrix is crucial since it dictates the feasibility and rules for carrying out operations such as adding or multiplying matrices. For instance, one can only add two matrices if they have the exactly same dimensions, and matrix multiplication requires that the number of columns in the first matrix match the number of rows in the second. Our present matrix B, for example, would be incompatible for multiplying by a matrix with dimensions other than 2xN, where N represents any number of columns.