(Special matricesB) ConstructB=B6and [Q,E] = eig(B). Verify thatE= eig(e) with eigenvalues 2∗ones(1,6)−2∗cos([0 : 5]∗pi/6) ine. How do you adjustQto produce the Discrete Cosine Transform with entriesDCT= cos([.5 : 5.5]′∗[0 :5]∗pi/6)/sqrt(3)

To construct matrix B6, you can use the following code in MATLAB:

B = [2 -1 0 0 0 0;
     -1 2 -1 0 0 0;
     0 -1 2 -1 0 0;
     0 0 -1 2 -1 0;
     0 0 0 -1 2 -1;
     0 0 0 0 -1 2];

[Q, E] = eig(B);

To verify that E and eig(e) are the same, you can use the following code:

e = 2*ones(1,6) - 2*cos([0:5]*pi/6);
isequal(round(E, 10), round(diag(e), 10))

This code will return a logical value, `true` if the eigenvalues are the same and `false` otherwise.

To adjust matrix Q to produce the Discrete Cosine Transform (DCT), you can use the following code:

DCT = cos([.5:5.5]'*[0:5]*pi/6)/sqrt(3);
Q_adjusted = Q*inv(DCT);

Here, `Q_adjusted` is the adjusted matrix Q that produces the DCT.