Approximate proju and projw. -8 -7 -6 -5 -4 -3 -2 -1 proj u 5.491 projw 4.801 = vector u vector w -5 -6 X X 1 3 Q
Approximate proju and projw. -8 -7 -6 -5 -4 -3 -2 -1 proj u 5.491 projw 4.801 = vector u vector w -5 -6 X X 1 3 Q
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 answer should be in matrix form:
![**Approximate \(\text{proj}_{\mathbf{w}}\mathbf{u}\) and \(\text{proj}_{\mathbf{u}}\mathbf{w}\).**
The graph above displays two vectors \(\mathbf{u}\) and \(\mathbf{w}\) on a coordinate plane. Vector \(\mathbf{u}\) is marked with a dashed green line, and vector \(\mathbf{w}\) is marked with a solid black arrow. They are positioned as follows:
- Vector \(\mathbf{u}\) originates from the point \((-1, 1)\) and points towards \((0, 0)\).
- Vector \(\mathbf{w}\) starts from \((0, 0)\) and extends to \((-1, -5)\).
On the graph, the task is to approximate the projections:
- \(\text{proj}_{\mathbf{w}}\mathbf{u}\)
- \(\text{proj}_{\mathbf{u}}\mathbf{w}\)
For the calculated approximations, it was found:
\[
\text{proj}_{\mathbf{w}}\mathbf{u} = 5.491 \quad (\text{Marked incorrect})
\]
\[
\text{proj}_{\mathbf{u}}\mathbf{w} = 4.801 \quad (\text{Marked incorrect})
\]
The representations and calculations likely involve projecting each vector onto the other, signifying how much one vector contributes in the direction of the other.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa35463d6-bfa8-46b5-8d12-2e8ead64b10c%2F6546f558-b8fb-4815-ada5-ea014f06bd88%2F9f4s8v_processed.png&w=3840&q=75)
Transcribed Image Text:**Approximate \(\text{proj}_{\mathbf{w}}\mathbf{u}\) and \(\text{proj}_{\mathbf{u}}\mathbf{w}\).**
The graph above displays two vectors \(\mathbf{u}\) and \(\mathbf{w}\) on a coordinate plane. Vector \(\mathbf{u}\) is marked with a dashed green line, and vector \(\mathbf{w}\) is marked with a solid black arrow. They are positioned as follows:
- Vector \(\mathbf{u}\) originates from the point \((-1, 1)\) and points towards \((0, 0)\).
- Vector \(\mathbf{w}\) starts from \((0, 0)\) and extends to \((-1, -5)\).
On the graph, the task is to approximate the projections:
- \(\text{proj}_{\mathbf{w}}\mathbf{u}\)
- \(\text{proj}_{\mathbf{u}}\mathbf{w}\)
For the calculated approximations, it was found:
\[
\text{proj}_{\mathbf{w}}\mathbf{u} = 5.491 \quad (\text{Marked incorrect})
\]
\[
\text{proj}_{\mathbf{u}}\mathbf{w} = 4.801 \quad (\text{Marked incorrect})
\]
The representations and calculations likely involve projecting each vector onto the other, signifying how much one vector contributes in the direction of the other.
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