1 - 5 Let a, = a2 = - 16 and b = For what value(s) of h is b in the plane spanned by a, and a,? 3 h The value(s) of h is(are) (Use a comma to separate answers as needed.)
1 - 5 Let a, = a2 = - 16 and b = For what value(s) of h is b in the plane spanned by a, and a,? 3 h The value(s) of h is(are) (Use a comma to separate answers as needed.)
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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![Let \(\mathbf{a_1} = \begin{bmatrix} 1 \\ 4 \\ -1 \end{bmatrix}\), \(\mathbf{a_2} = \begin{bmatrix} -5 \\ -16 \\ 3 \end{bmatrix}\), and \(\mathbf{b} = \begin{bmatrix} 4 \\ 0 \\ h \end{bmatrix}\). For what value(s) of \( h \) is \(\mathbf{b}\) in the plane spanned by \(\mathbf{a_1}\) and \(\mathbf{a_2}\)?
The value(s) of \( h \) is (are) [blank]. (Use a comma to separate answers as needed.)
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Explanation: This problem involves finding the values of \( h \) for which the vector \(\mathbf{b}\) is in the plane formed by the vectors \(\mathbf{a_1}\) and \(\mathbf{a_2}\). The task requires determining \( h \) such that \(\mathbf{b}\) can be expressed as a linear combination of \(\mathbf{a_1}\) and \(\mathbf{a_2}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F704a64b5-5250-41d0-9c29-5aaf5a50e535%2F9c86512c-64dd-4249-923f-ab037a1cc3a1%2Fvascvp_processed.png&w=3840&q=75)
Transcribed Image Text:Let \(\mathbf{a_1} = \begin{bmatrix} 1 \\ 4 \\ -1 \end{bmatrix}\), \(\mathbf{a_2} = \begin{bmatrix} -5 \\ -16 \\ 3 \end{bmatrix}\), and \(\mathbf{b} = \begin{bmatrix} 4 \\ 0 \\ h \end{bmatrix}\). For what value(s) of \( h \) is \(\mathbf{b}\) in the plane spanned by \(\mathbf{a_1}\) and \(\mathbf{a_2}\)?
The value(s) of \( h \) is (are) [blank]. (Use a comma to separate answers as needed.)
---
Explanation: This problem involves finding the values of \( h \) for which the vector \(\mathbf{b}\) is in the plane formed by the vectors \(\mathbf{a_1}\) and \(\mathbf{a_2}\). The task requires determining \( h \) such that \(\mathbf{b}\) can be expressed as a linear combination of \(\mathbf{a_1}\) and \(\mathbf{a_2}\).
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