4. Determine whether the given s (a) V = {x = (1, 22, 23) € (b) V = {x = (11, 12, 13) E (c) V = (x = (11, 12, 13) E (d) V = {set of all 3 x 3 dia

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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4. Determine whether the given set V is a vector space, justify your answer.
(a) V = (x = (1, 22, 23) € R³|*1*2 - 2x3 = 0}.
(b) V = (x = (11, 12, 13) € R³|9x1 + 4x2 - 3 = 0}.
(c) V = (x = (T1, T2, T3) ER³|3x1-1₂ + 7x3 = 1}.
(d) V = (set of all 3 x 3 diagonal matrices}.
Transcribed Image Text:4. Determine whether the given set V is a vector space, justify your answer. (a) V = (x = (1, 22, 23) € R³|*1*2 - 2x3 = 0}. (b) V = (x = (11, 12, 13) € R³|9x1 + 4x2 - 3 = 0}. (c) V = (x = (T1, T2, T3) ER³|3x1-1₂ + 7x3 = 1}. (d) V = (set of all 3 x 3 diagonal matrices}.
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