2331_Notes_3o1_fill - Math 2331 Linear Algebra Section 3.2...

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Math 2331 Linear Algebra Section 3.2 Solving Ax = 0 Matrices in Row Reduced Echelon Form An mxn augmented matrix is in row-reduced echelon form if it satisfies the following conditions: 1. Each row consisting entirely of zeros lies below any other row having nonzero entries. 2. The first nonzero entry in each row is 1 (called a leading 1 ). (the PIVOTS) 3. In any two successive (nonzero) rows, the leading 1 in the lower row lies to the right of the leading 1 in the upper row. 4. If a column contains a leading 1 (pivot), then the other entries in that column are zeros. Pivot Column: A column in the row reduced echelon form of coefficient matrix is a pivot column if one of the entries in the column is a 1 and the other entries are zeros. Example: Determine which of the following matrices are in row-reduced form. If a matrix is not in row-reduced form, state which condition is violated. a. 1000 0100 0012 ⎛⎞ ⎜⎟ ⎝⎠ e .
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2331_Notes_3o1_fill - Math 2331 Linear Algebra Section 3.2...

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