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+//page 187
+//Example 6.3
+clc;
+clear;
+close;
+disp('Standard ordered matrix for Linear operator T on R^3 is:');
+A = [5 -6 -6; -1 4 2; 3 -6 -4];
+disp(A,'A = ');
+disp('xI - A = ');
+B = eye(3,3);
+x = poly(0,"x");
+P = x*B - A;
+disp(P);
+disp('Applying row and column transformations:');
+disp('C2 = C2 - C3');
+P(:,2) = P(:,2) - P(:,3);
+disp('=>');
+disp(P);
+disp('Taking (x-2) common from C2');
+c = x-2;
+P(:,2) = P(:,2) / (x-2);
+disp('=>');
+disp(' * ', c);
+disp(P);
+disp('R3 = R3 + R2');
+P(3,:) = P(3,:) + P(2,:);
+disp('=>');
+disp(' * ', c);
+disp(P);
+P = [P(1,1) P(1,3); P(3,1) P(3,3)];
+disp('=>');
+disp(' * ', c);
+disp(P);
+disp('=>');
+disp(' * ',c);
+disp(det(P));
+disp('This is the characteristic polynomial');
+disp(A-B,'Now, A - I = ');
+disp(A-2*B,'And, A- 2I = ');
+disp(rank(A-B),'rank(A-I) = ');
+disp(rank(A-2*B),'rank(A-2I) = ');
+disp('W1,W2 be the spaces of characteristic vectors associated with values 1,2');
+disp('So by theorem 2, T is diagonalizable');
+a1 = [3 -1 3];
+a2 = [2 1 0];
+a3 = [2 0 1];
+disp(a1,'Null space of (T- I) i.e basis of W1 is spanned by a1 = ');
+disp('Null space of (T- 2I) i.e. basis of W2 is spanned by vectors x1,x2,x3 such that x1 = 2x1 + 2x3');
+disp('One example are;');
+disp(a2,'a2 = ');
+disp(a3,'a3 = ');
+disp('The diagonal matrix is:');
+D = [1 0 0 ;0 2 0;0 0 2];
+disp(D,'D = ');
+disp('The standard basis matrix is denoted as:');
+P = [a1;a2;a3]';
+disp(P,'P = ');
+disp(A*P,'AP = ');
+disp(P*D,'PD = ');
+disp('That is, AP = PD');
+disp('=>  inverse(P)*A*P = D');
+//end