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Mathematics-2014: Answer Writing Challenge – 3


13 September 2014


  1. 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.


  1. Determine whether or not the following vectors form a basis of R3:



  1. 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 α12 and α3.