Mathematics, 22.06.2019 17:20 gbrightwell

Determine whether the following sets are subspaces of r 3 under the operations of addition and scalar multiplication defined on r 3 . justify your answers. (a) w 1 = { ( a 1 , a 2 , a 3 ) ∈ r 3 : a 1 = 3 a 2 and a 3 = − a 2 } (b) w 2 = { ( a 1 , a 2 , a 3 ) ∈ r 3 : a 1 = a 3 + 2 } (c) w 3 = { ( a 1 , a 2 , a 3 ) ∈ r 3 : 2 a 1 − 7 a 2 + a 3 = 0 } (d) w 4 = { ( a 1 , a 2 , a 3 ) ∈ r 3 : a 1 − 4 a 2 − a 3 = 0 } (e) w 5 = { ( a 1 , a 2 , a 3 ) ∈ r 3 : a 1 + 2 a 2 − 3 a 3 = 1 } (f) w 6 = { ( a 1 , a 2 , a 3 ) ∈ r 3 : 5 a 2 1 − 3 a 2 2 + 6 a 2 3 = 0 }

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Determine whether the following sets are subspaces of r 3 under the operations of addition and scala...