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) Find a nonzero vector v with v € Span {0.0} 2 [1] [12]) and

) Find a nonzero vector v with v € Span {0.0} 2 [1] [12]) and

Advanced Engineering Mathematics
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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Find a nonzero vector **v** with **v** ∈ Span { \(\begin{bmatrix} 1 \\ 0 \\ 2 \end{bmatrix}\), \(\begin{bmatrix} 1 \\ 1 \\ 2 \end{bmatrix}\)} and ( \(\begin{bmatrix} 1 \end{bmatrix}\) \(\begin{bmatrix} 12 \end{bmatrix}\) )
Transcribed Image Text:Find a nonzero vector **v** with **v** ∈ Span { \(\begin{bmatrix} 1 \\ 0 \\ 2 \end{bmatrix}\), \(\begin{bmatrix} 1 \\ 1 \\ 2 \end{bmatrix}\)} and ( \(\begin{bmatrix} 1 \end{bmatrix}\) \(\begin{bmatrix} 12 \end{bmatrix}\) )
The text in the image is as follows: **v** ∈ Span { \[\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}, \begin{bmatrix} 12 \\ 8 \\ 21 \end{bmatrix} \] }. (In other words, **v** is in the intersection of the Span's.) **Explanation:** - The notation **v** ∈ Span indicates that the vector **v** is an element within the span of the given set of vectors. - The set inside the Span consists of two vectors: - The first vector is \[\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}\] - The second vector is \[\begin{bmatrix} 12 \\ 8 \\ 21 \end{bmatrix}\] - The statement explains that **v** is in the intersection of these spans, meaning **v** can be expressed as a linear combination of the vectors provided.
Transcribed Image Text:The text in the image is as follows: **v** ∈ Span { \[\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}, \begin{bmatrix} 12 \\ 8 \\ 21 \end{bmatrix} \] }. (In other words, **v** is in the intersection of the Span's.) **Explanation:** - The notation **v** ∈ Span indicates that the vector **v** is an element within the span of the given set of vectors. - The set inside the Span consists of two vectors: - The first vector is \[\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}\] - The second vector is \[\begin{bmatrix} 12 \\ 8 \\ 21 \end{bmatrix}\] - The statement explains that **v** is in the intersection of these spans, meaning **v** can be expressed as a linear combination of the vectors provided.
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