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- Augmented_matrix abstract "In linear algebra, an augmented matrix is a matrix obtained by appending the columns of two given matrices, usually for the purpose of performing the same elementary row operations on each of the given matrices.Given the matrices A and B, wherethe augmented matrix (A|B) is written asThis is useful when solving systems of linear equations. For a given number of unknowns, the number of solutions to a system of linear equations depends only on the rank of the matrix representing the system and the rank of the corresponding augmented matrix. Specifically, according to the Rouché–Capelli theorem, any system of linear equations is inconsistent (has no solutions) if the rank of the augmented matrix is greater than the rank of the coefficient matrix; if, on the other hand, the ranks of these two matrices are equal, the system must have at least one solution. The solution is unique if and only if the rank equals the number of variables. Otherwise the general solution has k free parameters where k is the difference between the number of variables and the rank; hence in such a case there are an infinitude of solutions.An augmented matrix may also be used to find the inverse of a matrix by combining it with the identity matrix.".
- Augmented_matrix wikiPageID "3676187".
- Augmented_matrix wikiPageRevisionID "594752835".
- Augmented_matrix hasPhotoCollection Augmented_matrix.
- Augmented_matrix subject Category:Matrices.
- Augmented_matrix type Abstraction100002137.
- Augmented_matrix type Arrangement107938773.
- Augmented_matrix type Array107939382.
- Augmented_matrix type Group100031264.
- Augmented_matrix type Matrices.
- Augmented_matrix type Matrix108267640.
- Augmented_matrix comment "In linear algebra, an augmented matrix is a matrix obtained by appending the columns of two given matrices, usually for the purpose of performing the same elementary row operations on each of the given matrices.Given the matrices A and B, wherethe augmented matrix (A|B) is written asThis is useful when solving systems of linear equations.".
- Augmented_matrix label "Augmented matrix".
- Augmented_matrix label "Matriz aumentada".
- Augmented_matrix label "مصفوفة ممتدة".
- Augmented_matrix label "增广矩阵".
- Augmented_matrix label "拡大行列".
- Augmented_matrix sameAs Matriz_aumentada.
- Augmented_matrix sameAs Matrize_zabaldu.
- Augmented_matrix sameAs 拡大行列.
- Augmented_matrix sameAs m.09tw8h.
- Augmented_matrix sameAs Q2750301.
- Augmented_matrix sameAs Q2750301.
- Augmented_matrix sameAs Augmented_matrix.
- Augmented_matrix wasDerivedFrom Augmented_matrix?oldid=594752835.
- Augmented_matrix isPrimaryTopicOf Augmented_matrix.