Math 103 Homework 4.3 Name 1) Determine if the polynomials are independent or dependent in the space of all polynomials of degree n, P. a) Pi(x) = 1, P2(x) = 2x, P3 (X) = 4-x b) P1 (x) = 1, P2(x) = 2x, P3(x) = 4-x2 2) Determine if the vectors in the set are linearly independent and if it is a basis for R . Explain. The vectors are linear independentot independent. The set is/ is not a basis for R3. The vectors are linear independentot independent. The set is/ is not a basis for R3. The vectors are linear independentot independent. The set is/ is not a basis for R3. 3) Find a basis for the space spanned by the given vectors V1, V2, ...Vs. Show your work. 4) Find a basis for the space spanned by the given vectors V1, V2, ...Vs. Show your work.5) Determine if the set (1, t, .., to } is a basis for Pn. 6) Let v1 = 7) Given A in and B in REF of A, find a basis for Nul A without using RREF calculator -3 1 -2 1 8) Given that A and B are row equivalent, find the bases for Nul A and Col A without using RREF calculator, A = 9) Given v1 - 3..2-31. 9-1231 2-3 - ce.. , and H= span {v1, v2, v3) and it can be verified that 4v1 + 5v2 - 3v3 = 0. Use this information to write a basis for H. 10) Let V be the vector space of functions, find a basis spanned by { sin t , sin 2t , sin t cost}