1.

Consider P2 (R) with the inner product = So f(x)g(x) dac With p1 (2) = 5x2 - 6 x + 3 and p2 (a) = 10 ac2 - 32 ac + 15 Use Gram-Schmidt to obtain a polynomial q(a) which lies in Span({p1 (a), p2 () }) and is orthogonal to p1 (a).2 o v o o 0 Performing GramSchmidt on 2 , 2 , in the order given, gives {101, 102, 1113}. Determine ml, 102 , 1 2 11 and 1133. Note: Entries of vectors must be integers or fractions, but not decimal numbers. a) What is 11:12? Consider C[0, 1] with the inner product 1 (f (a), ga) = f(x)g(x) dx Let v1 = ac - a2 and 12 = 15 + x - 51 x2 Applying Gram-Schmidt on {v1, U2 }, in order, gives { w1 , w2}. Determine w2 :Consider C 0, 1 with the inner product 1 (f (a) , g(2) = f(x)g(x) dx Let v1 = 3 + 4x + 10x2 and 72 = 3 - 20x + 42x2. Applying Gram-Schmidt on {v1, v2 }, in order, gives { w1, w2 }. Determine W2