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?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 21E

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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 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 P₁ R?

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