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(1) Consider (= ((a,ß)la.BER} Define addition and scalar multiplication on ( as follows: for each (a. B). (a',B') E and a E R, (a, B)+(a',B')-(a+ a',B+B') and a(a.B) (aa, aß) %3D Determine whether ( with the given operations is a vector space. Justify your answer. (ii) Let S (x,X2, Xz) where x, = (1,2,1), x, = (1,0, 2), x, = (1, 1,0). Does S span R? Explain briefly. %3D %3!

(1) Consider (= ((a,ß)la.BER} Define addition and scalar multiplication on ( as follows: for each (a. B). (a',B') E and a E R, (a, B)+(a',B')-(a+ a',B+B') and a(a.B) (aa, aß) %3D Determine whether ( with the given operations is a vector space. Justify your answer. (ii) Let S (x,X2, Xz) where x, = (1,2,1), x, = (1,0, 2), x, = (1, 1,0). Does S span R? Explain briefly. %3D %3!

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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(1) Consider (= ((a,ß)la.ßER} Define addition and scalar multiplication on ( as follows: for each (a. B). (a', B') EC and a E R. (a, ß)+(a',B')-(a+ a',B + B') and a(a.B) (aa, aß) %3D Determine whether ( with the given operations is a vector space. Justify your answer. (11) Let S (x,X2, X3) where x, = (1,2,1), x (1,0, 2), x, = (1, 1,0). Does S span R? Explain briefly. %3D %3D
Transcribed Image Text:(1) Consider (= ((a,ß)la.ßER} Define addition and scalar multiplication on ( as follows: for each (a. B). (a', B') EC and a E R. (a, ß)+(a',B')-(a+ a',B + B') and a(a.B) (aa, aß) %3D Determine whether ( with the given operations is a vector space. Justify your answer. (11) Let S (x,X2, X3) where x, = (1,2,1), x (1,0, 2), x, = (1, 1,0). Does S span R? Explain briefly. %3D %3D
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