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5 -3,ã3 = Let đ1 = a2 = 9. (a) Calculate žā1 – žā2 and comment on what you notice about the result in terms of the vector ãz (b) Based on your observation in (a), show that the set {ã1, d2, ā3} is linearly dependent by writing down a linear dependence relation on ả1, ả2, ã3 5 5 5 (c) Now let A = 1 -3 7. Based on your answer in part (b) give a non-zero vector i = r2 such that 7 4 |X3 A = 0 (d) Do the columns of A span R³? Why or why not?

5 -3,ã3 = Let đ1 = a2 = 9. (a) Calculate žā1 – žā2 and comment on what you notice about the result in terms of the vector ãz (b) Based on your observation in (a), show that the set {ã1, d2, ā3} is linearly dependent by writing down a linear dependence relation on ả1, ả2, ã3 5 5 5 (c) Now let A = 1 -3 7. Based on your answer in part (b) give a non-zero vector i = r2 such that 7 4 |X3 A = 0 (d) Do the columns of A span R³? Why or why not?

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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5 -3,ã3 = Let đ1 = a2 = 9. (a) Calculate žā1 – žā2 and comment on what you notice about the result in terms of the vector ãz (b) Based on your observation in (a), show that the set {ã1, d2, ā3} is linearly dependent by writing down a linear dependence relation on ả1, ả2, ã3 5 5 5 (c) Now let A = 1 -3 7. Based on your answer in part (b) give a non-zero vector i = r2 such that 7 4 |X3 A = 0 (d) Do the columns of A span R³? Why or why not?
Transcribed Image Text:5 -3,ã3 = Let đ1 = a2 = 9. (a) Calculate žā1 – žā2 and comment on what you notice about the result in terms of the vector ãz (b) Based on your observation in (a), show that the set {ã1, d2, ā3} is linearly dependent by writing down a linear dependence relation on ả1, ả2, ã3 5 5 5 (c) Now let A = 1 -3 7. Based on your answer in part (b) give a non-zero vector i = r2 such that 7 4 |X3 A = 0 (d) Do the columns of A span R³? Why or why not?
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