This question concerns the following matrix: A = [6,sort(3)],[sqrt(3),4]. This matrix is symmetric so it can be orthogonally diagonalised.

a) Enter the eigenvalues ofAin increasing order,separated by commas.This question accepts lists of numbers or formulas separated by semicolons. E.g. "2; 4; 6" or "x+1; x-1". The order of the list doesnt matter but be sure to separate the terms with semicolons. b)Find an eigenvector for each eigenvalue. Enter these eigenvectors as a list, e.g. [0,1],[1,0]. c)For each eigenvalue,find an orthonormal basis for the eigenspaceE. LetPbe a matrix with these orthonormal eigenvectors as columns. Enter the matrixP,as a list of row vectors For each eigenvalue,find an orthonormal basis for the eigenspaceE. LetPbe a matrix with these orthonormal eigenvectors as columns. Enter the matrixP,as a list of row vector d)Enter the matrix product (P^T)AP(as per part (c)).