Punjab Engineering College 2010 B.E Ma102 mid term - Question Paper

Mid-Term I Examination ( MA 102) Roll No

M Marks : 15 Time Allowed : 1 Hour

If Wj and W2 are subspaces of a vector space V, then does their union and intersection form a subspace of V ? Justify your answer.

Extend S = {(0,1,0,2, 1)} to a basis for V = the subspace of R⁵ consisting of all vectors of the form (a, b, c, d, e) , where c = a, b = d + e.

Let S = {t² + 1, t 2, t + 3} and T = {21² + t, t² + 3 , t} be bases for P₂. Let v = 81² 4t + 6 . Find [i7]₅ ,[v]_t , P_S<__T and verify [v]_s = P_s+-_T Mr

Prove that a linear transformation L 'V -> VK is 1-1 iff Ker L = {0}.

Let L : Pi - P₂ defined by L(t + 1) = t² + t + 2 , L(t - 1) = t + 2 . Find L(at + b) using the matrix of L with respect to the basis

S = { t + 1, t 1} and T = {t² + 1 ,t ,t - 1).