• Linear Systems
• Gauss
• Cramer's Rule
• Solving
• Homogeneous
• Parameters

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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3.

Study and resolve the system, if possible:

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