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ANSWER BOTH QUESTIONS ACCRUATELY AND CORRECTLY FOR A GOOD RATING Q5. Consider any vector space

`V`

. Let

`x,y,z`

be elements of

`V`

and

`a,b`

be scalars. (a) Prove: If

`x+y=x+z`

then

`y=z`

. (b) Prove:

`(a+b)(x+y)=ax+bx+ay+by`

. Q6. Consider polynomials with complex coefficients and degree at most

`n`

.

`P_(n)(C)={a_(0)+a_(1)x+a_(2)x^(2)+cdots+a_(n)x^(n):a_(i)inC}`

Prove that

`P_(n)(C)`

is a vector space. (Hint: summation notation will simplify your argument.)