## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 8 - Section 8.2 - Inconsistent and Dependent Systems and Their Applications - Concept and Vocabulary Check - Page 902: 3

#### Answer

Thre are infinitely many solutions

#### Work Step by Step

Convert the last row in the equation. Translating row 3 of the matrix into equation form, we obtain, $0x+0y+0z=0$ $0=0$ This row does not add any information about the variable. Thus, drop it from the system which can be expressed as $\left[ \left. \begin{matrix} \begin{matrix} 1 & -1 & -2 \\ \end{matrix} \\ \begin{matrix} 0 & 1 & -10 \\ \end{matrix} \\ \end{matrix} \right|\begin{matrix} 2 \\ -1 \\ \end{matrix} \right]$ Convert it in equation, \begin{align} x-y-2z=2 & \\ y-10=-1 & \\ \end{align} Here, we have two equations and three variables so, we have an infinite number of solutions for these equations.

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