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2. Consider the set of vectors in R4 S = {(1, 0,-1, 1), (2, -1, 0, 1), (1, 1, 2, 1)}. (a) Determine if (1, 3, 3, 2) is in the span (S). In your answer: i. Derive a system of linear equations to be solved. ii. Solve the system using row operations. Indicate which row operations you used. iii. If possible, write (1, 3, 3, 2) as a linear combination of vectors in S. (b) Determine if S is linearly independent or linearly dependent.

2. Consider the set of vectors in R4 S = {(1, 0,-1, 1), (2, -1, 0, 1), (1, 1, 2, 1)}. (a) Determine if (1, 3, 3, 2) is in the span (S). In your answer: i. Derive a system of linear equations to be solved. ii. Solve the system using row operations. Indicate which row operations you used. iii. If possible, write (1, 3, 3, 2) as a linear combination of vectors in S. (b) Determine if S is linearly independent or linearly dependent.

Advanced Engineering Mathematics
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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2. Consider the set of vectors in R4 S = {(1, 0,-1, 1), (2,−1, 0, 1), (1, 1, 2, 1)}. (a) Determine if (1, 3, 3, 2) is in the span (S). In your answer: i. Derive a system of linear equations to be solved. ii. Solve the system using row operations. Indicate which row operations you used. iii. If possible, write (1, 3, 3, 2) as a linear combination of vectors in S. (b) Determine if S is linearly independent or linearly dependent.
Transcribed Image Text:2. Consider the set of vectors in R4 S = {(1, 0,-1, 1), (2,−1, 0, 1), (1, 1, 2, 1)}. (a) Determine if (1, 3, 3, 2) is in the span (S). In your answer: i. Derive a system of linear equations to be solved. ii. Solve the system using row operations. Indicate which row operations you used. iii. If possible, write (1, 3, 3, 2) as a linear combination of vectors in S. (b) Determine if S is linearly independent or linearly dependent.
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Step 1: Introduction of the given problem

S equals open curly brackets open parentheses 1 comma 0 comma negative 1 comma 1 close parentheses comma open parentheses 2 comma negative 1 comma 0 comma 1 close parentheses comma open parentheses 1 comma 1 comma 2 comma 1 close parentheses close curly brackets

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