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  3. please answer only number 4 not number 3 you need...

Question: please answer only number 4 not number 3 you need...

Question details
Please answer ONLY number 4 not Number 3
You need to know 3 in order to answer 4 tho
3: Let V be a vector space over a field F and W a subspace of V. For any v e V, consider the set (v} + W = {u + w I w e W}. We will denote it simply as u + w. Now consider the set We can define addition and scalar multiplication on this set by (u + W) + (w + W) (u + w) + W , and λ(v+W)=Aw+W. Prove that V/W is a vector space. It is called the quotient of V by W. 4. Let С[z] be the vector space of polynonials and let ll-span {r. I a > 2). (a) Find a set of 3 linearly independent elements of Clr)/w. (b) Find 2 nonzero elements p, q Cir] that are linearly independant and such that p+ W and q+W are linearly dependant and nonzero. Note: you can only receive full points for this problem if your polynomials p and q and different from everyone elses! If you understand the problem then this will be easy to ensure. Please urite your two polynomials very large on the top of your homework
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