Let B = {b₁,b₂} and C = = {C₁, C₂}. Find [v] and [v]. 98 6+ 10 [v]. [v] 8 9 -8 -7 -6 = b2 c2 bl Lo -2 et 5 4 3 2 1 -1 -2 -3 -4 -5- -6 + 2 8 9 10 H 12 13 14
Let B = {b₁,b₂} and C = = {C₁, C₂}. Find [v] and [v]. 98 6+ 10 [v]. [v] 8 9 -8 -7 -6 = b2 c2 bl Lo -2 et 5 4 3 2 1 -1 -2 -3 -4 -5- -6 + 2 8 9 10 H 12 13 14
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
![The image depicts a coordinate grid with vectors and two distinct bases:
- **Bases**:
- \(\mathcal{B} = \{ \mathbf{b_1}, \mathbf{b_2} \} \)
- \(\mathcal{C} = \{ \mathbf{c_1}, \mathbf{c_2} \} \)
- **Objective**: Find the coordinates of vector \(\mathbf{v}\) with respect to bases \(\mathcal{B}\) and \(\mathcal{C}\).
### Graph Explanation:
- **Grid**:
- The grid has horizontal and vertical lines with coordinates labeled from \(-10\) to \(14\) on the x-axis and from \(-6\) to \(6\) on the y-axis.
- **Vectors**:
- \(\mathbf{b_1}\) and \(\mathbf{b_2}\) are represented with purple arrows.
- \(\mathbf{c_1}\) and \(\mathbf{c_2}\) are represented with orange arrows.
- \(\mathbf{v}\) is a black arrow extending from the origin to point \((8, 1)\).
### Task:
- **Determine**:
- \([\mathbf{v}]_{\mathcal{B}}\)
- \([\mathbf{v}]_{\mathcal{C}}\)
### Answer Boxes:
- **Coordinates with Respect to \(\mathcal{B}\)**:
\[
[\mathbf{v}]_{\mathcal{B}} = \boxed{}
\]
- **Coordinates with Respect to \(\mathcal{C}\)**:
\[
[\mathbf{v}]_{\mathcal{C}} = \boxed{}
\]
To find these coordinates, observe where \(\mathbf{v}\) aligns with the grid lines determined by each basis, considering their direction and magnitude.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa35463d6-bfa8-46b5-8d12-2e8ead64b10c%2Ffb0c631a-f3ca-439e-8884-00a8b22a6b62%2Foldapm6_processed.png&w=3840&q=75)
Transcribed Image Text:The image depicts a coordinate grid with vectors and two distinct bases:
- **Bases**:
- \(\mathcal{B} = \{ \mathbf{b_1}, \mathbf{b_2} \} \)
- \(\mathcal{C} = \{ \mathbf{c_1}, \mathbf{c_2} \} \)
- **Objective**: Find the coordinates of vector \(\mathbf{v}\) with respect to bases \(\mathcal{B}\) and \(\mathcal{C}\).
### Graph Explanation:
- **Grid**:
- The grid has horizontal and vertical lines with coordinates labeled from \(-10\) to \(14\) on the x-axis and from \(-6\) to \(6\) on the y-axis.
- **Vectors**:
- \(\mathbf{b_1}\) and \(\mathbf{b_2}\) are represented with purple arrows.
- \(\mathbf{c_1}\) and \(\mathbf{c_2}\) are represented with orange arrows.
- \(\mathbf{v}\) is a black arrow extending from the origin to point \((8, 1)\).
### Task:
- **Determine**:
- \([\mathbf{v}]_{\mathcal{B}}\)
- \([\mathbf{v}]_{\mathcal{C}}\)
### Answer Boxes:
- **Coordinates with Respect to \(\mathcal{B}\)**:
\[
[\mathbf{v}]_{\mathcal{B}} = \boxed{}
\]
- **Coordinates with Respect to \(\mathcal{C}\)**:
\[
[\mathbf{v}]_{\mathcal{C}} = \boxed{}
\]
To find these coordinates, observe where \(\mathbf{v}\) aligns with the grid lines determined by each basis, considering their direction and magnitude.
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