---**Problem Statement:**Find the value(s) of $ h $ for which the vectors are linearly dependent. Justify your answer.\[\left[\begin{array}{r}1 \\-2 \\-4\end{array}\right], \quad\left[\begin{array}{r}-4 \\9 \\8\end{array}\right], \quad\left[\begin{array}{r}2 \\1 \\h\end{array}\right]\]**Answer Format:**The value(s) of $ h $ which make the vectors linearly dependent is(are) $ \_\_\_\_ $ because this will cause $ \_\_\_\_ $ to be a $ \_\_\_\_ $ variable. (Use a comma to separate answers as needed.)**Dropdown Options:**- $ x_3 $- $ x_1 $- $ x_2 $- pivot- free\---Explanation of Graph (if it were present):If there were any graphical elements or diagrams present, an explanation would follow here, but the provided image only contains matrices and a textual problem, so no additional diagram explanations are necessary.---

Vectors are Linearly Dependent so it (two vector) can be written as a linear combination of third…

Answered: Find the value(s) of h for which the…

Math

Advanced Math

Find the value(s) of h for which the vectors are linearly dependent. Justify your answer. -4 2 - 4 8.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

100%

---

**Problem Statement:**

Find the value(s) of $ h $ for which the vectors are linearly dependent. Justify your answer.

\[
\left[\begin{array}{r}
1 \\
-2 \\
-4
\end{array}\right], \quad
\left[\begin{array}{r}
-4 \\
9 \\
8
\end{array}\right], \quad
\left[\begin{array}{r}
2 \\
1 \\
h
\end{array}\right]
\]

**Answer Format:**

The value(s) of $ h $ which make the vectors linearly dependent is(are) $ \_\_\_\_ $ because this will cause $ \_\_\_\_ $ to be a $ \_\_\_\_ $ variable.

(Use a comma to separate answers as needed.)

**Dropdown Options:**

- $ x_3 $
- $ x_1 $
- $ x_2 $

- pivot
- free
\---

Explanation of Graph (if it were present):

If there were any graphical elements or diagrams present, an explanation would follow here, but the provided image only contains matrices and a textual problem, so no additional diagram explanations are necessary.

---

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