Also is it a free or basic variable? Find the value(s) of h for which the vectors are linearly dependent. Justify your answer.6.- 4- 346.11h.....because this will causeto be avariable.The value(s) of h which makes the vectors linearly dependent is(are)(Use a comma to separate answers as needed.)X1X2X3

The given vectors are 3-36,6-911,-44h. The objective is to determine the values of h that makes…

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

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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Question

Also is it a free or basic variable?

Find the value(s) of h for which the vectors are linearly dependent. Justify your answer.
6.
- 4
- 3
4
6.
11
h
.....
because this will cause
to be a
variable.
The value(s) of h which makes the vectors linearly dependent is(are)
(Use a comma to separate answers as needed.)
X1
X2
X3

Expert Solution

Step 1

The given vectors are $[\begin{matrix} 3 \\ - 3 \\ 6 \end{matrix}], [\begin{matrix} 6 \\ - 9 \\ 11 \end{matrix}], [\begin{matrix} - 4 \\ 4 \\ h \end{matrix}]$ .

The objective is to determine the values of $h$ that makes these vectors linearly dependent.

The set of vectors $u, v, w \in ℝ^{3}$ are linearly dependent, if and only if the matrix formed by keeping these vectors as columns of the matrix, that is, $A = [u v w]$ is singular.