1)Let V be a vector space with addition denoted by + and scalar multiplication denoted by * ,and let vector v0 be a fixed vector selected from V.

(v0 = v subscript 0)

Define a new addition on V by: u+v = u+v+v0

Define a new scalar mult. on V by: c*v = c*v+(c-1)*v0

Show that V with + and * as its operations is a vector space by proving that all 10 axioms are satisfied and explain why this new vector is or is not a subspace of the original vector space.

(v0 = v subscript 0)

Define a new addition on V by: u+v = u+v+v0

Define a new scalar mult. on V by: c*v = c*v+(c-1)*v0

Show that V with + and * as its operations is a vector space by proving that all 10 axioms are satisfied and explain why this new vector is or is not a subspace of the original vector space.

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