March 2026
Intermediate
512 pages
14h 19m
English
Content preview from Mathematics in Cybersecurity
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5Introduction to Systems of Linear Equations
5.1 Definition and Notation of Systems of Linear Equations
A system of linear equations is a collection of two or more linear equations that share the same set of variables. In other words, a system of linear equations is a set of equations where each equation describes a linear relationship between the same set of variables.
Mathematically, a system of n linear equations in m variables can be expressed as:
where aij and bi are real numbers (some possibly zero), and x1, x2, …, xm are the variables.
The values aij represent the weights or coefficients of the variables, and the constants bi are isolated on the right-hand side of each equation.
When we say there is a “linear relationship” among the variables, we mean the equations are linear equations: each of the variables appears to the power 1 only and is not multiplied against other variables. In a graphical sense, the equations represent lines only in the two-dimensional case. When more than two variables appear, the equations have graphs that lie in higher-dimensional space and ...
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