13 September 2014
- Find whether the vectors 2x3+x2+x+1, x3+3x2+x-2, x3+2x2-x+3 of R[x], the vector space of all polynomials over the real number field , are linearly independent or not.
- Determine whether or not the following vectors form a basis of R3:
(1,1,2),(1,2,5),(5,3,4).
- Show that the vectors α1=(1,0,-1),α2=(1,2,1),α3=(0,3,-2) form a basis of R3.Express each of the standard basis vectors as a linear combination of α1,α2 and α3.
