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Let V be the set of all ordered n -tuple...

Let V be the set of all ordered n -tuples `V={(a_1,a_2,……..a_n):a_1,a_2,……a_n} si F}` under the operation of addition and scalar multiplication in V defined as
Let `a=(a_1,a_2,…….a_n),b=(b_1,b_2……b_n)` then a,b belongs to V
`a+b=(a_1+b_1,a_2+b_2.......a_n+b_n)siV`
II Let a=(a_1,a_2,.......a_n) si V` and `asiF` than `alphaa=(alphaa_1,alphaa_2,....alphaa_n)si V`

A

V is a vector space under the defined operation of addition and scalar multiplication

B

V is not a vector space under the defined operation of addition and scalar multiplication

C

V under the defined operation of addition is not abelian group.

D

V under the defined operation of multiplication is not an abelian group.

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • Given the mapping f:V_3(F) rarr V_2(F) defined by f(a_1,a_2,a_3)=(a_1,a_2)

    A
    f is homomorphism of `V_3(F) onto `V_2(F)`
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    `a_1^2`+a_2^2+….,+a_n^2 ge 1/n`
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    `a_1^2` +a_2^2+…,+a_n^2 le 1/n`
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    `a_1^2 +a_2^2….,+a_n^2 ge n`
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