Question: For each, list three elements and then show it is a vector space. (a) The set of linear polynomials P1 = {a0 + a1x |

For each, list three elements and then show it is a vector space.
(a) The set of linear polynomials P1 = {a0 + a1x | a0, a1 ∈ R} under the usual polynomial addition and scalar multiplication operations.
(b) The set of linear polynomials {a0 + a1x | a0 - 2a1 = 0}, under the usual polynomial addition and scalar multiplication operations.
Use Example 1.3 as a guide. Most of the ten conditions are just verifications.

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a Three elements are 1 2x 2 1x and x Of course many answers are possible The verification is just like Example 13 We first do conditions 15 from Definition 11 having to do with addition For closure un... View full answer

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