Linear Algebra:

Question 2. Let V be the vector space of polynomials with degree 5 3, and p1 =t3+2t2+3t+9, p2 =2t3+t2 5t+6, p3 =3t34t27t3. (a) Is the polynomial p=8t315t27t12 a linear combination of 111,102, and p3? If yes, write p as a linear combination of 101,192, and p3. If not, explain why not. (b) Is the polynomial p=8t315t27t a linear combination of 111,102, and p3? If yes, write p as a linear combination of 111,192, and p3. If not, explain why not. (c) Are the vectors $91,132,313 linearly independent? (d) Does the set {111,192,113} span V? (e) Is the set {111,102,103} a basis of V