## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 10 - 10.1 - Matrices and Systems of Equations - 10.1 Exercises - Page 711: 83

#### Answer

x = -2a y = a z = a w = 0 Where a is any real number

#### Work Step by Step

The reduced row-echelon form of the matrix is: $\begin{bmatrix} 1 & 0 & 2 & 0 & |0\\ 0 & 1 & -1 & 0 & |0\\ 0 & 0 & 0 & 1 & |0\\ \end{bmatrix}$ We can write the solution as: x + 2z = 0 y - z = 0 w = 0 We then can write the system in terms of z: x = -2z y = z w = 0 To not use one of the variables in the system we can use a: x = -2a y = a z = a w = 0 Where a is any real number

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