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- If there are n unknowns in the system of equations and ρ (A) = ρ ([A|B]) = n then the system AX = B, is consistent and has a unique solution. Case 2 : If there are n unknowns in the system AX = B ρ (A) = ρ ([A| B]) < n then the system is consistent and has infinitely many solutions and these solutions.
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Sep 5, 2016 · Determine Whether a System of Equations is Consistent. This is very simple. This requires two steps. Convert to Row-Eschilon Form. Check if the last column is a pivot column. If it is, it's inconsistent. If it isn't, it's consistent . Brief Explanation
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Sep 17, 2022 · A consistent linear system of equations will have exactly one solution if and only if there is a leading 1 for each variable in the system. If a consistent linear system of equations has a free variable, it has infinite solutions.
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.
HOW TO CHECK CONSISTENCY OF LINEAR EQUATIONS USING MATRICES. Write down the given system of equations in the form of a matrix equation AX = B. Step 1 : Find the augmented matrix [A, B] of the system of equations. Step 2 : Find the rank of A and rank of [A, B] by applying only elementary row operations. Note :
Solution: To check the condition of consistency we need to find out the ratios of the coefficients of the given equations, \ (\begin {array} {l}\frac {a_1} {a_2} = \frac {1} {2}\end {array} \) \ (\begin {array} {l}\frac {b_1} {b_2} = \frac {1} {2}\end {array} \) \ (\begin {array} {l}\frac {c_1} {c_2} = \frac {1} {2}\end {array} \)
Mar 15, 2015 · 1) The system is consistent when $A$ and $A$ extended with $b_m$ as another column has the same rank. If the system is consistent then if $n > m$ it is not informationally complete, if $n = m$, 2) The linear system is informationally complete when $A$ is invertible.
One of the easiest ways to find solutions of systems of linear equations (or show no solutions exist) is Gauss (or Gauss-Jordan) Row Reduction; it amounts to doing the kind of things you did, but in a systematic, algorithmic, recipe-like manner.
