Jordan

# Jordan - A Matrix Method to Solve a System of n Linear...

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A Matrix Method to Solve a System of n Linear Equations in n unknowns: 1. Write the augmented matrix that represents the system. 2. Perform row operations to simplify the augmented matrix to one having zeros below the diagonal of the coefficient portion of the matrix. (An entry is on the diagonal of the coefficient portion of the matrix if it is located in row i and column i for some positive integer i n.) If the augmented matrix is equivalent to a matrix with zeros below the diagonal and all non-zero entries on the diagonal , then the corresponding system has a unique solution . If the aumented matrix is equivalent to a matrix with zeros below the diagonal and at least one zero on the diagonal , then the corresponding system does not have a unique solution In this case, examination of the rows which contain a zero on the diagonal entry will determine whether the corresponding system has no solution or an infinite number of solutions.

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Examples: The system of equations represented by the following
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Jordan - A Matrix Method to Solve a System of n Linear...

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