3 hence we assume a1 has the form a1 x1 x2 x3 x4 for

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Unformatted text preview: −15 4 −3 −−−−−−−−− Replace R3 with −4R1 + R3 0 −15 4 5 3 The matrix equivalent of ‘triangular form’ is row echelon form. The reader is encouraged to refer to Definition 8.3 for comparison. Note that the analog of ‘leading variable’ of an equation is ‘leading entry’ of a row. Specifically, the first nonzero entry (if it exists) in a row is called the leading entry of that row. Definition 8.4. A matrix is said to be in row echelon form provided all of the following conditions hold: 1. The first nonzero entry in each row is 1. 2. The leading 1 of a given row must be to the right of the leading 1 of the row above it. 3. Any row of all zeros cannot be placed above a row with nonzero entries. To solve a system of a linear equations using an augmented matrix, we encode the system into an augmented matrix and apply Gaussian Elimination to the rows to get the matrix into row-echelon form. We then decode the matrix and back substitute. The next example illustrates this nicely. Exampl...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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