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MAThe Gauss-Jordan elimination method is an algorithm used to solve systems of linear equations and find matrix inverses by transforming an augmented matrix into reduced row echelon form. It extends Gaussian elimination by using elementary row operations to create a diagonal matrix (often an identity matrix on the left side). Key Features and Process: Goal: Convert the system \(Ax=b\) into a form where the coefficient matrix \(A\) becomes an identity matrix, making the solutions (\(x,y,z\)) directly readable.Row Operations: Uses three main operations: swapping rows, multiplying a row by a non-zero scalar, and adding/subtracting multiples of rows.Reduction Steps: Unlike Gaussian elimination (which only creates an upper triangular matrix), Gauss-Jordan reduces all entries above and below each pivot (diagonal element) to zero.Application: Ideal for solving systems with three or more variables and finding the inverse of matrices.
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