The Rouche-Capelli Theorem is a result of linear algebra that determines the number of solutions of a system of linear equations from the ranks of its coefficient matrix and its augmented matrix. The same result is known under several other names depending on country, including the Kronecker-Capelli theorem, the Rouche-Fontene theorem, the Rouche-Frobenius theorem, and simply the Frobenius theorem.
Facts
StatementA system of linear equations with n variables and coefficients in a field K has a solution if and only if its coefficient matrix A and its augmented matrix [A|b] have the same rank. 1 Classification
Statement Form Statement FormCharacterization Theorem 1 Connections
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Sources
1. Rouche-Capelli theorem (Wikipedia)
Statement
has a solution if and only if its coefficient matrix A and its augmented matrix [A|b] have the same rank
In Group: Linear Algebra and Matrix Theory, Lead section
Rouché-Capelli theorem is a theorem in linear algebra that determines the number of solutions of a
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