College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 6, Matrices and Determinants - Section 6.1 - Matrices and Systems of Linear Equations - 6.1 Exercises - Page 500: 14


a.$\quad$ the matrix is in row-echelon form. b.$\quad$the matrix is not in reduced row-echelon form. c.$\quad\left\{\begin{array}{lll} x & +3y & =-3\\ & y & =5 \end{array}\right.$

Work Step by Step

$a.$ 1. The first nonzero number in each row (reading from left to right) is 1. 2. The leading entry in the 2nd row is to the right of the leading entry in the row immediately above it. 3. There are no rows consisting entirely of zeros. Answer: the matrix is in row-echelon form. b. 4. Not every number above and below each leading entry is a 0. (there is a 3 above the leading 1 in the second row) Answer: the matrix is not in reduced row-echelon form. c. The augmented matrix has rows representing each equation. Two rows, two equations. Each row contains the coefficients of the variables on the LHS, followed by the constant of the RHS: $\left\{\begin{array}{lll} x & +3y & =-3\\ & y & =5 \end{array}\right.$
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