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 make the system consistent.

Mar 30, 2019 · Consistent linear system. Ask Question Asked 6 years, 1 month ago. Modified 6 years, 1 month ago. Viewed ...

Mar 15, 2015 · 1.) The very basic definition for consistency is determined by the last column of the augmented matrix. The last column must not be a pivot column after writing the matrix in row reduced echelon form.

Apr 13, 2019 · It means we have a linear transformation, and a desired result, and we want to know whether we can find an input to the linear transformation that gives us the desired result as a result. The transformation has an image.

Jan 9, 2018 · An augmented matrix contains the coefficients of a system of linear equations. It consists of the coefficients of the LHS (all terms with variables), with the coefficients of the RHS (all terms without variables) "stuck on" at the right - hence the name "augmented".

is inconsistent because the first line represents a linear equation $0x+0y=-10$, i.e. $0=-10$, which is a contradiction. Geometrically, when you solve a 2x2 linear system, you are finding the intersection between a pair of lines. If you reach a contradiction, like the system above, then your lines do not intersect, i.e. they must be parallel.

linear system consistent. Ask Question Asked 11 years, 2 months ago. Modified 11 years, 2 months ago ...

Else, the system is consistent. Consistency simplyy means: Can all equations simultaneously be true? If so, then the system is consistent. If not, then it is inconsistent. When a system is inconsistent, no solution can possibly exist. When it is consistent, either a unique solution exists, or infinitely many solutions exist.

Sep 8, 2017 · For more complex situations, the criterion for consistency is this: the matrix of the l.h.s. of the linear system and the augmented matrix have the same rank. $\endgroup$ – Bernard Commented Sep 7, 2017 at 19:57

Sep 5, 2019 · Every such row stands for an equation of the type, $$\text{pivot variable equals linear combination of free variables, plus constant}$$ The free variables, if there are any, can be given arbitrary values; the equations then determine the values of the pivot variables, and give a solution to the original system of equations. So, if there are any ...