Q2) determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail a) The set of all real numbers with...

Extracted text: Q2) determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail a) The set of all real numbers with the standard operations of addition and multiplication. b) The set of all pairs of real numbers of the form (x, y), where x > 0, with the standard operations on R2.


Extracted text: Q3) > In Exercises 17–18, first show that the set S = {p|, P2» P3} is a basis for P2, then express p as a linear combination of the vectors in S, and then find the coordinate vector of p relative to S. 17. p, = 1+x +x²| P2 = x +x², p, = x²; p= 7-x+2x² 18. p, = 1+2x +x², p2 = 2+9x, P3 = 3+ 3x + 4.x²; p= 2+17x – 3x²