l_notes32 - 1 Lecture XXXII Row Reduction Determinants Row...

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Unformatted text preview: 1 Lecture XXXII Row Reduction; Determinants Row Reduction Recall the 3 elementary operations we will use to solve the system of equations AX = D : ( α ) multiplying an equation by a non-zero scalar; ( β ) adding to an equation some multiple of a different equation; ( γ ) interchanging two equations. We call the matrix [ A : D ] the augmented matrix of the system AX = D . We will use α, β, and γ to bring B = [ A : D ], or, in the case of homogeneous systems, B = A to a row-reduced form . Definition 1 The row-reduced form of a matrix B is a matrix obtained from B by applying the elementary operations that has the following properties: 1. Every non-zero row has 1 as its first non-zero element from left to right. This element is called the pivot of the row. 2. Each pivot occurs in a column to the right of all pivots from upper rows. 3. All zero rows are at the bottom of the matrix. 4. For any pivot, all other elements in its column are equal to zero....
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This note was uploaded on 09/24/2011 for the course MATH 1802 taught by Professor Duorg during the Two '04 term at Macquarie.

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l_notes32 - 1 Lecture XXXII Row Reduction Determinants Row...

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