matrices - How to tell if a linear system is consistent - Mathematics ...
The system is inconsistent if your matrix contains any of this: $$\begin{bmatrix} 0 & 0 & 0 &| &\text{non-zero number} \end{bmatrix}$$ Thus, we need the right side to be $0$ in order to …
What is a consistent linear system? + Example - Socratic
2016年5月3日 · A consistent linear system is a system of linear equations with at least one set of values satisfying all equations. A system of linear equations is said to be consistent if there is …
linear algebra - what do free variable and leading variables mean ...
2014年3月21日 · The terms "leading variable" and "free variable" are usually defined for the matrix representing a system, and only when the matrix is in row-echelon form. The …
algebraic geometry - moving part and fixed part of a linear system ...
For dimension 3 and more nothing like this is true: look up the definition of "movable linear system".-Any rational map can be extended to codimension 1. In your situation, the rational …
How many solutions can a system of linear equations have?
2014年10月22日 · With linear systems of equations, there are three possible outcomes in terms of number of solutions: One solution. Infinitely many solutions. No Solutions at all. If there is one …
Linear Systems with Multiplication - Algebra - Socratic
Yes. Any linear system of #n# equations in #n# variables can be solved by this method: #ax+by=c# #dx+ey=f#. Mutiply the first equation by #d# and the second by #-a# to get: …
Linear system and base points - Mathematics Stack Exchange
2022年8月5日 · The first line of the proof talks about the linear system $|P+Q|$ having dimension $1$ and is base point-free.
How to solve a system of linear equations modulo n?
First you can multiply the system by any number that has an inverse, that is $\gcd(x,20)=1$. So in particular you cannot multiply or divide by $2,4,5,10$ as you would not multiply or divide by …
algebraic geometry - The morphism introduced by a linear system ...
2018年1月30日 · Morphism of a linear system contracting curves. 3. What is the morphism associated to a divisor? 1.
Finding nonnegative solutions to an underdetermined linear system
This is a standard linear optimization problem. To summarize, the set of all nonnegative solutions can be completely described by either a finite system of linear inequalities, or a finite …