The only dierence between the two processes is what

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Unformatted text preview: eave it to the reader to check. As part of Gaussian Elimination, we used row operations to obtain 0’s beneath each leading 1 to put the matrix into row echelon form. If we also require that 0’s are the only numbers above a leading 1, we have what is known as the reduced row echelon form of the matrix. Definition 8.5. A matrix is said to be in reduced row echelon form provided both of the following conditions hold: 1. The matrix is in row echelon form. 2. The leading 1s are the only nonzero entry in their respective columns. 470 Systems of Equations and Matrices Of what significance is the reduced row echelon form of a matrix? To illustrate, let’s take the row echelon form from Example 8.2.1 and perform the necessary steps to put into reduced row echelon form. We start by using the leading 1 in R3 to zero out the numbers in the rows above it. 1 2 −1 4 120 3 Replace R1 with R3 + R1 4 0 1 −4 0 −− − − − − − − − 0 1 0 − − − − − − − −→ 7 7 4 Rep...
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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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