(Solved): Question 2 [7+3+(2+6+1+3) marks] (a) Let w be the subspace of R spanned by the vectors. u (1.0.0. ...

Question 2 [7+3+(2+6+1+3) marks] (a) Let w be the subspace of Rª spanned by the vectors. u (1.0.0.1), (1,0,1,2), u =(-1.1.2.1) .Use the Gram-Schmidt process to find an orthogonal basis for W and state the dimension of W. (b) Let V be the subspace spanned by the orthogonal basis ((1,0,-1), (0, 1,0);. Find the vector in W closest to the vector (2,3,1). Mathematics IB, EC, 202103 1) Use the characteristic equation to find the eigenvalues of A. 2) For each eigenvalue find a corresponding eigenvector. 3) Give a matrix P that will orthogonally diagonalise A, and the diagonal matrix D that results. 4) Use your diagonalization to find A. (c) Let A be the matrix 4 =