Consider the set, S = {(5, 0, 3), (10, 0, 7), (0, 5, 0)} Answer the following questions. Your work must clearly show the justification of your conclusion. There are various methods that this can be done (some can be combined to answer more than one question). Be sure to cite any theorems or definitions. Give your conclusion in a complete sentence. Be sure your answer connects all the dots to lead to that conclusion. For this question, you may use technology to fill in the gaps for any computations (i.e. for finding a determinant or putting a matrix in reduced row echelon form); you must state what technology you used and for what purpose. Be sure you show the statements that are bridged by your technology -- such as the original matrix and then equal to the RRE form. a. Is the set S linearly independent? b. Does the set S span R3? c. Is v = (1, 2, 1) in the span of S? If so, give the coordinates v(s). If not, show why not.
Consider the set, S = {(5, 0, 3), (10, 0, 7), (0, 5, 0)} Answer the following questions. Your work must clearly show the justification of your conclusion. There are various methods that this can be done (some can be combined to answer more than one question). Be sure to cite any theorems or definitions. Give your conclusion in a complete sentence. Be sure your answer connects all the dots to lead to that conclusion. For this question, you may use technology to fill in the gaps for any computations (i.e. for finding a determinant or putting a matrix in reduced row echelon form); you must state what technology you used and for what purpose. Be sure you show the statements that are bridged by your technology -- such as the original matrix and then equal to the RRE form. a. Is the set S linearly independent? b. Does the set S span R3? c. Is v = (1, 2, 1) in the span of S? If so, give the coordinates v(s). If not, show why not.
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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Transcribed Image Text:Consider the set, \( S = \{(5, 0, 3), (10, 0, 7), (0, 5, 0)\} \)
Answer the following questions. Your work must clearly show the justification of your conclusion. There are various methods that this can be done (some can be combined to answer more than one question). Be sure to cite any theorems or definitions. **Give your conclusion in a complete sentence. Be sure your answer connects all the dots to lead to that conclusion.**
*For this question, you may use technology to fill in the gaps for any computations (i.e. for finding a determinant or putting a matrix in reduced row echelon form); you must state what technology you used and for what purpose. Be sure you show the statements that are bridged by your technology -- such as the original matrix and then equal to the RRE form.*
a. Is the set \( S \) linearly independent?
b. Does the set \( S \) span \( \mathbb{R}^3 \)?
c. Is \( v = (1, 2, 1) \) in the span of \( S \)? If so, give the coordinates \( v_{(S)} \). If not, show why not.
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