Initial Post Prompt Let S = {(3,-1,2), (4, 2, 1), (-3, 1, 0), (2, 2, 2)} and T= {7-4x, 5x} Include the following in your initial post: Justify all of your reasoning using theorems and calculations: For S: • Does the set of vectors span R^3? • Are the set of vectors linearly independent? • Does the set of vectors form a basis for R^3? For T: • Does the set of vectors span P₁ R? • Is the set linearly independent or dependent? Does the set form a basis for P₁R?
Initial Post Prompt Let S = {(3,-1,2), (4, 2, 1), (-3, 1, 0), (2, 2, 2)} and T= {7-4x, 5x} Include the following in your initial post: Justify all of your reasoning using theorems and calculations: For S: • Does the set of vectors span R^3? • Are the set of vectors linearly independent? • Does the set of vectors form a basis for R^3? For T: • Does the set of vectors span P₁ R? • Is the set linearly independent or dependent? Does the set form a basis for P₁R?
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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Can you please Show all of your work And answer all of the questions on the picture, Thank you!
![**Initial Post Prompt**
Let
\[ S = \{(3, -1, 2), (4, 2, 1), (-3, 1, 0), (2, 2, 2)\} \]
and
\[ T = \{7 - 4x, 5x\} \]
**Include the following in your initial post:**
Justify all of your reasoning using theorems and calculations:
For **S**:
- Does the set of vectors span \( \mathbb{R}^3 \)?
- Are the set of vectors linearly independent?
- Does the set of vectors form a basis for \( \mathbb{R}^3 \)?
For **T**:
- Does the set of vectors span \( P_{1}\mathbb{R} \)?
- Is the set linearly independent or dependent?
- Does the set form a basis for \( P_{1}\mathbb{R} \)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0655393b-8df3-4633-b13c-e0d6983d2306%2F90782b81-335d-4464-be80-f56f4e1c2047%2F9e1ekx_processed.png&w=3840&q=75)
Transcribed Image Text:**Initial Post Prompt**
Let
\[ S = \{(3, -1, 2), (4, 2, 1), (-3, 1, 0), (2, 2, 2)\} \]
and
\[ T = \{7 - 4x, 5x\} \]
**Include the following in your initial post:**
Justify all of your reasoning using theorems and calculations:
For **S**:
- Does the set of vectors span \( \mathbb{R}^3 \)?
- Are the set of vectors linearly independent?
- Does the set of vectors form a basis for \( \mathbb{R}^3 \)?
For **T**:
- Does the set of vectors span \( P_{1}\mathbb{R} \)?
- Is the set linearly independent or dependent?
- Does the set form a basis for \( P_{1}\mathbb{R} \)?
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Can you please answer the same question but show all of your work ON PICTURES! Explain step by step. DO NOT WRITE IT LIKE THE PERSON DID. POST YOUR WORK ON PICTURES.
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