1 The matrix A = -1 4 has eigenvalue 3. Which of the following -1 1 is aa basis of the 3-eigenspace? 1 -1 -2 1 1 1 (| 1) 0 ) 1 () 1 -1 -2 4.

-4 -2) -2) - Let A = -4 5. 2 , Vュー and v2 = Verify that v and v2 are %3D -2 eigenvectors of A. Then orthogonally diagonalize A.

Find a basis for the eigenspace corresponding to the eigenvalue. 4 - 3 3 A = 6 , 1 = 3 - 2 -6 -3 A basis for the eigenspace corresponding to 1 = 3 is { }. (Type a vector or list of vectors. Type an integer or simplified fraction for each matrix element. Use a comma to separate answers as needed.)

Consider the matrix 2 -4 A = (-²₁ 2¹) -1 (a) Compute the eigenvalues and the corresponding eigenvectors. (b) Let v = = [2, 1], compute A10¹0000 V.