Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Solve this linear algebra multiple chhoice question, it deals with linear indepence and dependence.

**Question:**

For what values of \( h \) are the vectors

\[
\begin{bmatrix}
1 \\
1 \\
1 \\
h^2 + h - 1
\end{bmatrix}, 
\begin{bmatrix}
1 \\
2 \\
2 \\
h + 1
\end{bmatrix}, 
\begin{bmatrix}
1 \\
3 \\
4 \\
h + 2
\end{bmatrix}, \, \text{and} \,
\begin{bmatrix}
1 \\
4 \\
8 \\
h + 3
\end{bmatrix}
\]

linearly dependent?

**Options:**

- \( h = -1 \)
- \( h = 1 \)
- \( h \) can be any real number.
- No such values for \( h \).
- \( h = -1 \) and \( h = 1 \)

**Answer:**

\[
\boxed{h = -1 \, \text{and} \, h = 1}
\]
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Transcribed Image Text:**Question:** For what values of \( h \) are the vectors \[ \begin{bmatrix} 1 \\ 1 \\ 1 \\ h^2 + h - 1 \end{bmatrix}, \begin{bmatrix} 1 \\ 2 \\ 2 \\ h + 1 \end{bmatrix}, \begin{bmatrix} 1 \\ 3 \\ 4 \\ h + 2 \end{bmatrix}, \, \text{and} \, \begin{bmatrix} 1 \\ 4 \\ 8 \\ h + 3 \end{bmatrix} \] linearly dependent? **Options:** - \( h = -1 \) - \( h = 1 \) - \( h \) can be any real number. - No such values for \( h \). - \( h = -1 \) and \( h = 1 \) **Answer:** \[ \boxed{h = -1 \, \text{and} \, h = 1} \]
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