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

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 8E

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