What vector v is given by the coordinate vector B = -21 - -5 1 1 -2 -5] -5 4 {JEJEJEJ} -5 3 -1 3 ? 5 5
What vector v is given by the coordinate vector B = -21 - -5 1 1 -2 -5] -5 4 {JEJEJEJ} -5 3 -1 3 ? 5 5
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Problem Statement:**
What vector **v** is given by the coordinate vector:
\[
\begin{bmatrix}
-2 \\
-5 \\
1 \\
1
\end{bmatrix}_{\mathcal{B}}
\]
**Basis Set:**
\[
\mathcal{B} = \left\{
\begin{bmatrix}
3 & -1 \\
-3 & 6
\end{bmatrix},
\begin{bmatrix}
2 & 5 \\
-5 & 3
\end{bmatrix},
\begin{bmatrix}
-2 & -5 \\
-1 & 3
\end{bmatrix},
\begin{bmatrix}
-5 & 4 \\
5 & 5
\end{bmatrix}
\right\}
\]
**Explanation:**
The image presents a problem of finding the vector **v** which is expressed in terms of a given coordinate vector with respect to a specified basis \(\mathcal{B}\). The basis \(\mathcal{B}\) consists of four 2x2 matrices. The coordinate vector is a column matrix with elements \([-2, -5, 1, 1]\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa35463d6-bfa8-46b5-8d12-2e8ead64b10c%2F4d721a84-5fb4-454f-b4ea-56509dadef0d%2Fo0jrfx_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
What vector **v** is given by the coordinate vector:
\[
\begin{bmatrix}
-2 \\
-5 \\
1 \\
1
\end{bmatrix}_{\mathcal{B}}
\]
**Basis Set:**
\[
\mathcal{B} = \left\{
\begin{bmatrix}
3 & -1 \\
-3 & 6
\end{bmatrix},
\begin{bmatrix}
2 & 5 \\
-5 & 3
\end{bmatrix},
\begin{bmatrix}
-2 & -5 \\
-1 & 3
\end{bmatrix},
\begin{bmatrix}
-5 & 4 \\
5 & 5
\end{bmatrix}
\right\}
\]
**Explanation:**
The image presents a problem of finding the vector **v** which is expressed in terms of a given coordinate vector with respect to a specified basis \(\mathcal{B}\). The basis \(\mathcal{B}\) consists of four 2x2 matrices. The coordinate vector is a column matrix with elements \([-2, -5, 1, 1]\).
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