Let B = {b₁,b2} and = {C₁, C₂}. Find [v] and [v]. B 10 -9 [v] Ⓡ [v] 8 -7 -6 -5 -4 -3 -2 -1 6- 5 4 3 2 y -H+ -2 -3 -4 -5 bx c2 62 13 cl 4 5 6 7 8 9 10 11 12 13 14
Let B = {b₁,b2} and = {C₁, C₂}. Find [v] and [v]. B 10 -9 [v] Ⓡ [v] 8 -7 -6 -5 -4 -3 -2 -1 6- 5 4 3 2 y -H+ -2 -3 -4 -5 bx c2 62 13 cl 4 5 6 7 8 9 10 11 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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![Let \(\mathcal{B} = \{ \mathbf{b_1}, \mathbf{b_2}\} \) and \(\mathcal{C} = \{ \mathbf{c_1}, \mathbf{c_2}\} \). Find \([\mathbf{v}]_{\mathcal{B}}\) and \([\mathbf{v}]_{\mathcal{C}}\).
**Graph Explanation:**
The graph shows a grid with two sets of lines, intersecting at various points:
1. **Axes and Grid:**
- The x-axis ranges from -10 to 14, and the y-axis ranges from -6 to 6.
- Grid lines are drawn along these axes.
2. **Vectors:**
- \(\mathbf{v}\): Originating from the origin \((0, 0)\) and extending to approximately \((14, 6)\).
- \(\mathbf{b_1}\): Extends from the origin in the negative direction, approximately to \((-2, -3)\).
- \(\mathbf{b_2}\): Extends from the origin to approximately \((1, 3)\).
- \(\mathbf{c_1}\): Extends from the origin to approximately \((3, -2)\).
- \(\mathbf{c_2}\): Extends from the origin to approximately \((2, 3)\).
3. **Intersections:**
- Lines of different colors (orange and purple) form a lattice.
- The purple lines are parallel to \(\mathbf{b_1}\) and \(\mathbf{b_2}\).
- The orange lines are parallel to \(\mathbf{c_1}\) and \(\mathbf{c_2}\).
**Boxes for Input:**
Below the graph are two boxes where the results for \([\mathbf{v}]_{\mathcal{B}}\) and \([\mathbf{v}]_{\mathcal{C}}\) are to be entered.
\[
[\mathbf{v}]_{\mathcal{B}} = \text{[input box]}
\]
\[
[\mathbf{v}]_{\mathcal{C}} = \text{[input box]}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa35463d6-bfa8-46b5-8d12-2e8ead64b10c%2Fe9d10af2-49f3-4e54-96f2-e79c6d80f92e%2F4n8vas8_processed.png&w=3840&q=75)
Transcribed Image Text:Let \(\mathcal{B} = \{ \mathbf{b_1}, \mathbf{b_2}\} \) and \(\mathcal{C} = \{ \mathbf{c_1}, \mathbf{c_2}\} \). Find \([\mathbf{v}]_{\mathcal{B}}\) and \([\mathbf{v}]_{\mathcal{C}}\).
**Graph Explanation:**
The graph shows a grid with two sets of lines, intersecting at various points:
1. **Axes and Grid:**
- The x-axis ranges from -10 to 14, and the y-axis ranges from -6 to 6.
- Grid lines are drawn along these axes.
2. **Vectors:**
- \(\mathbf{v}\): Originating from the origin \((0, 0)\) and extending to approximately \((14, 6)\).
- \(\mathbf{b_1}\): Extends from the origin in the negative direction, approximately to \((-2, -3)\).
- \(\mathbf{b_2}\): Extends from the origin to approximately \((1, 3)\).
- \(\mathbf{c_1}\): Extends from the origin to approximately \((3, -2)\).
- \(\mathbf{c_2}\): Extends from the origin to approximately \((2, 3)\).
3. **Intersections:**
- Lines of different colors (orange and purple) form a lattice.
- The purple lines are parallel to \(\mathbf{b_1}\) and \(\mathbf{b_2}\).
- The orange lines are parallel to \(\mathbf{c_1}\) and \(\mathbf{c_2}\).
**Boxes for Input:**
Below the graph are two boxes where the results for \([\mathbf{v}]_{\mathcal{B}}\) and \([\mathbf{v}]_{\mathcal{C}}\) are to be entered.
\[
[\mathbf{v}]_{\mathcal{B}} = \text{[input box]}
\]
\[
[\mathbf{v}]_{\mathcal{C}} = \text{[input box]}
\]
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