Exercise 1 -- Eigenvalues & Eigenvectors 1A B = randi([-8,8],4,4) % The command tril returns (fill in the blank here) A1 = tril(B) The eigenvalues of A1 are ... beacuse (state the theorem here) % Find eigenvalues and eigenvectors using eig: % P is (give a description here) % D is (give a description here) [P,D] = eig(A1) % check if A1 = P*D*inv(P) (Yes or No) P*D*inv(P) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Check whether P*D*inv(P) = A1. If not, A1 is not diagonalizable. Keep your % previous work, re-generate another matrix B and repeat the process until % A1 is diagonalizable. %B = randi([-8,8],4,4) %A1 = tril(B) %[P,D] = eig(A1) %P*D*inv(P) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Find eigenvalues and eigenvectors using eigvec: [P,D] = eigvec(A1) % check if A1 = P*D*inv(P)? (Yes or No) P*D*inv(P) Conclusion: A1 is diagonalizable since