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 of A in 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 λ,find an orthonormal basis for the eigenspace Eλ.

Let Pbe a matrix with these orthonormal eigenvectors as columns. 

Enter the matrix P,as a list of row vectors

For each eigenvalue λ,find an orthonormal basis for the eigenspace Eλ.

Let P be a matrix with these orthonormal eigenvectors as columns. 

Enter the matrix P,as a list of row vector

d) Enter the matrix product (P^T)AP (as per part (c)).