Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 10 - Section 10.3 - Matrices and Systems of Linear Equations - 10.3 Exercises - Page 710: 43

Answer

Inconsistent.

Work Step by Step

$ \begin{bmatrix} 1 & -1 & 3 & 3\\ 4 & -8 & 32 & 24\\ 2 & -3 & 11 & 4 \end{bmatrix} $ Add -4 times the 1st row to the 2nd row to produce a new 2nd row. Add -2 times the 1st row to the 3rd row to produce a new 3rd row. $ \begin{bmatrix} 1 & -1 & 3 & 3\\ 0 & -4 & 20 & 12\\ 0 & -1 & 5 & -2 \end{bmatrix} $ Interchange the 2nd and the 3rd row. $ \begin{bmatrix} 1 & -1 & 3 & 3\\ 0 & -1 & 5 & -2\\ 0 & -4 & 20 & 12 \end{bmatrix} $ Divide the second row by -1. $ \begin{bmatrix} 1 & -1 & 3 & 3\\ 0 & 1 & -5 & 2\\ 0 & -4 & 20 & 12 \end{bmatrix} $ Add 4 times the 2nd row to the 3rd row. $ \begin{bmatrix} 1 & -1 & 3 & 3\\ 0 & 1& -5 & 2\\ 0 & 0 & 0& 20 \end{bmatrix} $ From the last row we got the equation $0=20$ which is false and therefore the system is inconsistent.
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