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Consider the set V of all real triples of the form (a, b, c) where c = a - 2b under the usual vector addition and scalar multiplication of R3 Let v1 = (a1, b1, C1), v2 =(a2, b2, C2), be vectors in set V as needed (pay attention to the definition of vectors in this set, i.e. the relationship between c and the other components -- it should be incorporated in your proof.), and let k be a scalar. Either: prove that this set V is a subspace of R or show that V is not a vector subspace by giving a counter example to a required condition. Be clear in what you need to show; show it; and then state your conclusion

Consider the set V of all real triples of the form (a, b, c) where c = a - 2b under the usual vector addition and scalar multiplication of R3 Let v1 = (a1, b1, C1), v2 =(a2, b2, C2), be vectors in set V as needed (pay attention to the definition of vectors in this set, i.e. the relationship between c and the other components -- it should be incorporated in your proof.), and let k be a scalar. Either: prove that this set V is a subspace of R or show that V is not a vector subspace by giving a counter example to a required condition. Be clear in what you need to show; show it; and then state your conclusion

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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Consider the set V of all real triples of the form (a, b, c) where c = a - 2b under the usual vector addition and scalar multiplication of R3 Let v1 = (a1, b1, C1), v2 =(a2, b2, c2), be vectors in set V as needed (pay attention to the definition of vectors in this set, i.e. the relationship between c and the other components -- it should be incorporated in your proof.), and let k be a scalar. Either: prove that this set V is a subspace of R3 or show that V is not a vector subspace by giving a counter example to a required condition. Be clear in what you need to show; show it; and then state your conclusion
Transcribed Image Text:Consider the set V of all real triples of the form (a, b, c) where c = a - 2b under the usual vector addition and scalar multiplication of R3 Let v1 = (a1, b1, C1), v2 =(a2, b2, c2), be vectors in set V as needed (pay attention to the definition of vectors in this set, i.e. the relationship between c and the other components -- it should be incorporated in your proof.), and let k be a scalar. Either: prove that this set V is a subspace of R3 or show that V is not a vector subspace by giving a counter example to a required condition. Be clear in what you need to show; show it; and then state your conclusion
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