2 and 3 plz

2. (i) Let v C([0,1]) with the inner product = So f(t) g(t) dt. Let W be the subspace spanned by the linearly independent set {t, vt}. Find an orthonormal basis for W. [2+2) (ii) Consider R3(R) with the standard inner product. Let W be a subspace generated by the vectors (1,1,0) and (0,1,1). Find the space of all vectors in R3 that are perpendicular to every vector in W. [3] (iii) Show that skew-symmetric has eigenvalues are either zero or purely imaginary. [3] 3 1 - 1 3. (i) Let A = 13 - 1 Find all the eigenvalues and the corresponding eigenvectors of 3 3 -1 A. Also mention the algebraic multiplicities and geometric multiplicities of the eigenvalues of A and conclude whether A is diagonalizable or not. I [2 + 4 + 1] 2 2 2 2 2 2 2 2 2 2 2 25 NN COCK (ii) Find the largest eigenvalue of the matrix [3] IN