# 10_3 - Section 10.3 A Matrix Method to solve a system of n...

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Section 10.3: A Matrix Method to solve a system of n linear equations in n variables Instructor: Ms. Hoa Nguyen 1 Augmented Matrix 2 Solve System of Linear Equations by Matrices The idea is very similar to the method of elimination, i.e., replacing the original augmented matrix of the system with the EQUIVALENT matrix whose lower triangle contains only zeros. The lower triangle refers to the entries under the diagonal of the matrix. Rules for Obtaining an Equivalent Matrix (Row Operations) 1. Interchange any two rows. 2. Multiply (or divide) each row by a NONZERO constant. 3. Replace a row by the sum (or difference) of the row and a NONZERO multiple of another row. Example 1 : 1

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The steps of solving a linear system by the matrix method : Write the augmented matrix that represents the given system. Perform row operations to obtain the EQUIVALENT matrix whose lower triangle contains only zeros.
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