Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 0-32198-238-X
ISBN 13: 978-0-32198-238-4

Chapter 1 - Linear Equations in Linear Algebra - 1.1 Exercises: 20

Answer

The system is consistent for all $h$.

Work Step by Step

We begin with matrix $\begin{bmatrix} 1 & h & -3 \\ -2 & 4 & 6 \\ \end{bmatrix}$ First, we need to multiply the first row by $2$ and add it to the second row: $\begin{bmatrix} 1 & h & -3 \\ 0 & 2h+4 & 0 \\ \end{bmatrix}$ Write $c$ for $2h+4$. Then the second equation $c\cdot x_2 = 0$ has a solution for every value of $c$. So the system is consistent for all $h$.
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