3. Consider the following subset SCR' 1 1 S= 8 (a) Is span(S) = R*? Explain your reasoning and show work to justify your answer. (b) Determine if S is linearly dependent or independent. Explain why. -2 -1 (c) i. If possible, write as a linear combination of vectors in S. 6. ii. Is this linear combination unique? Why or why not, explain your reasoning.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 22EQ
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I need this Linear Algebra and Fourier Analysis course question solve.

3. Consider the following subset S CR
{]
1
2
1
-3
0.
1
1
-4
S =
-2
-10
8
(a) Is span(S) = R*? Explain your reasoning and show work to justify your answer.
(b) Determine if S is linearly dependent or independent. Explain why.
-2
-1
(c) i. If possible, write
as a linear combination of vectors in S.
ii. Is this linear combination unique? Why or why not, explain your reasoning.
(d) Find two vectors u, v e R*, if possible, such that u ¢ span(S) but v E span(S).
Justify your answer.
Transcribed Image Text:3. Consider the following subset S CR {] 1 2 1 -3 0. 1 1 -4 S = -2 -10 8 (a) Is span(S) = R*? Explain your reasoning and show work to justify your answer. (b) Determine if S is linearly dependent or independent. Explain why. -2 -1 (c) i. If possible, write as a linear combination of vectors in S. ii. Is this linear combination unique? Why or why not, explain your reasoning. (d) Find two vectors u, v e R*, if possible, such that u ¢ span(S) but v E span(S). Justify your answer.
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