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4s -3ss, t in R -t d 12

4s -3ss, t in R -t d 12

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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(A) find a basis, (b) state the dimension
The image presents a mathematical set notation for vectors, likely from a linear algebra or vector space context. It reads: 2. \(\left\{ \begin{bmatrix} 4s \\ -3s \\ -t \end{bmatrix} : s, t \in \mathbb{R} \right\}\) This expression describes a set of vectors in three-dimensional space, where the components of each vector are defined by the parameters \(s\) and \(t\), both of which are real numbers (\(\mathbb{R}\)). The vectors in this set take the form: - The first component is \(4s\). - The second component is \(-3s\). - The third component is \(-t\). The set includes all possible combinations of \(s\) and \(t\), indicating that it represents a subset of \(\mathbb{R}^3\), possibly a plane or a line, depending on additional context regarding linear dependencies or other constraints that might be described elsewhere in the material.
Transcribed Image Text:The image presents a mathematical set notation for vectors, likely from a linear algebra or vector space context. It reads: 2. \(\left\{ \begin{bmatrix} 4s \\ -3s \\ -t \end{bmatrix} : s, t \in \mathbb{R} \right\}\) This expression describes a set of vectors in three-dimensional space, where the components of each vector are defined by the parameters \(s\) and \(t\), both of which are real numbers (\(\mathbb{R}\)). The vectors in this set take the form: - The first component is \(4s\). - The second component is \(-3s\). - The third component is \(-t\). The set includes all possible combinations of \(s\) and \(t\), indicating that it represents a subset of \(\mathbb{R}^3\), possibly a plane or a line, depending on additional context regarding linear dependencies or other constraints that might be described elsewhere in the material.
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