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7. Suppose you wish to show that the set of vectors is linearly dependent. 3 9 1 , 8 4 9 -69 6 49 3 8 32 (a) Enter a matrix A which can help you show this and use rref on it. (b) Explain how you can tell from the rref that the vectors are linearly dependent. (c) * Give a nontrivial linear combination of the vectors which yields 0. (Hint: Make a free variable nonzero.) (d) Find a theorem in §1.7 which allows us to conclude, without doing any of the previous compu- tations, that this set must be linearly dependent. (e) Does this set of vectors span R4? Justify your answer.

7. Suppose you wish to show that the set of vectors is linearly dependent. 3 9 1 , 8 4 9 -69 6 49 3 8 32 (a) Enter a matrix A which can help you show this and use rref on it. (b) Explain how you can tell from the rref that the vectors are linearly dependent. (c) * Give a nontrivial linear combination of the vectors which yields 0. (Hint: Make a free variable nonzero.) (d) Find a theorem in §1.7 which allows us to conclude, without doing any of the previous compu- tations, that this set must be linearly dependent. (e) Does this set of vectors span R4? Justify your answer.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 8E
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7. Suppose you wish to show that the set of vectors is linearly dependent. 3 9 1 , 8 4 9 -69 6 49 3 8 32 (a) Enter a matrix A which can help you show this and use rref on it. (b) Explain how you can tell from the rref that the vectors are linearly dependent. (c) * Give a nontrivial linear combination of the vectors which yields 0. (Hint: Make a free variable nonzero.) (d) Find a theorem in §1.7 which allows us to conclude, without doing any of the previous compu- tations, that this set must be linearly dependent. (e) Does this set of vectors span R4? Justify your answer.
Transcribed Image Text:7. Suppose you wish to show that the set of vectors is linearly dependent. 3 9 1 , 8 4 9 -69 6 49 3 8 32 (a) Enter a matrix A which can help you show this and use rref on it. (b) Explain how you can tell from the rref that the vectors are linearly dependent. (c) * Give a nontrivial linear combination of the vectors which yields 0. (Hint: Make a free variable nonzero.) (d) Find a theorem in §1.7 which allows us to conclude, without doing any of the previous compu- tations, that this set must be linearly dependent. (e) Does this set of vectors span R4? Justify your answer.
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