Solving Systems of Equations
The necessary and sufficient condition for a system of m equations and n unknowns has a solution where the range of the coefficient matrix and the augmented matrix are equal.
- r = r' Consistent system.
- r = r' = n Consistent independent system.
- r = r'≠ n Consistent dependent system.
- r ≠ r' Inconsistent system.
Steps to Solve a System of Equations
1. Find the rank of the matrix of coefficients:
r(A) = 3
2. Find the rank of the augmented matrix:
r(A') = 3
3. Study the obtained information and determine which type of system it is:
4. Solve the system if it is not inconsistent, by Cramer's rule or the Gauss elimination method.
Take the system corresponding to the submatrix of order 3, which has a rank of 3 and solve it:
Examples
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Study and resolve the system, if possible:
Subject
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