An independent system of linear equations is a set of vectors in Rm, where any other vector in Rm can be written as a linear combination of all of the vectors in the set. The vector equation and the matrix equation can only have the trivial solution (x=0).
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A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
A "system" of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.
The answer will depend on what kinds of equations: there are linear equations, polynomials of various orders, algebraic equations, trigonometric equations, exponential ones and logarithmic ones. There are single equations, systems of linear equations, systems of linear and non-linear equations. There are also differential equations which are classified by order and by degree. There are also partial differential equations.
The answer depends on whether they are linear, non-linear, differential or other types of equations.
Any solution to a system of linear equations must satisfy all te equations in that system. Otherwise it is a solution to AN equation but not to the system of equations.