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- A system of linear equations is said to be consistent if there is a solution which satisfies all of the equations. For example, { (x+y = 1), (x+2y = 5):} has the solution { (x = -3), (y = 4):} and thus is consistent.
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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.
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} \)
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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.
A linear system is consistent if and only if its coefficient matrix has the same rank as does its augmented matrix (the coefficient matrix with an extra column added, that column being the column vector of constants).
Apr 21, 2015 · If a linear system involves n variables, x1,x2,..xn, then the solution set will take one of the following n + 2 forms: (0) The empty set. The system is inconsistent and has no solutions. (1) A unique solution in the form of an n -tuple. (2) A line of solutions expressible as: x1 = a1 ⋅ t + b1. x2 = a2 ⋅ t + b2. ... xn = an ⋅ t + bn. for all t ∈ R.
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