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7. Suppose you wish to show that the set of vectors 4 000000 -1 2 -3 -24 44 11 is linearly dependent. (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 4 000000 -1 2 -3 -24 44 11 is linearly dependent. (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.

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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7. Suppose you wish to show that the set of vectors 4 -9 -17 4 08H000 1 4 -5 (e) 4 3 3 4 3 −14 is linearly dependent. (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. Does this set of vectors span R¹? Justify your answer.
Transcribed Image Text:7. Suppose you wish to show that the set of vectors 4 -9 -17 4 08H000 1 4 -5 (e) 4 3 3 4 3 −14 is linearly dependent. (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. Does this set of vectors span R¹? Justify your answer.
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