c is a 3x3 matrix with exactly two distinct eigenvalues. 1, and 2. Which of the...
Question 1 1 pts Cis a 3x3 matrix with exactly two distinct eigenvalues, 11 and 12. Which of the following are possibilities for the algebraic and geometric multiplicities of l, and 12 as eigenvalues of C? (select ALL that apply) It is possible that 11 has algebraic multiplicity 2 and geometric multiplicity 2, and X2 has algebraic multiplicity 1 and geometric multiplicityo. It is possible that X has algebraic multiplicity 2 and geometric multiplicity 1, and 12 has algebraic multiplicity...
(1 point) Suppose a 3 x 3 matrix A has only two distinct eigenvalues. Suppose that tr(A) = 1 and det(A) = 63. Find the eigenvalues of A with their algebraic multiplicities. The smaller eigenvalue has multiplicity and the larger eigenvalue has multiplicity
Question 1: Question 2: Thx, will give a thumb Determine the algebraic and geometric multiplicity of each eigenvalue of the matrix. 2 3 3 3 2 3 3 3 2 Identify the eigenvalue(s). Select the correct choice below and fill in the answer box(es) to complete your choice. O A. There is one distinct eigenvalue, 1 = OB. There are two distinct eigenvalues, hy and 12 (Use ascending order.) OC. There are three distinct eigenvalues, 14 , 22 = (Use...
-2 2 4 2-5 (10 pts) The matrix C 12 3 has two distinct eigenvalues. AI < has multiplicity 2 and has multiplicity -2 2 4 2-5 (10 pts) The matrix C 12 3 has two distinct eigenvalues. AI
16. Assume that M is a 4 x 4 matrix with eigenvalues 11 = -1, 12 = 0, 13 = 5, y = 1. Choose the correct answer(s) (a) A basis of R* can be formed using eigenvectors of M (b) The matrix M is nonsingular c) The matrix M is diagonalizable (d) All of the above 17. Let S be a 3 x 3 symmetric matrix whose eigenvalues are 12 = 4, 13 = -1. Choose the correct answer(s)...
Determine the algebraic and geometric multiplicities of the eigenvalues for the following matrix. B = 13 71 has characteristic equation (3-1)(6 - 1) = 0 LO 6] First determine the eigenvalues, order them from smallest to greatest: 11 = 12 = Now determine the algebraic and geometric multiplicities for each eigenvalue above. You can do this with direct computation or using any of the theorems discussed in class to avoid computation. ab(11) = YB(11) = ab(12) = YB(12) = We...
92 (a) The matrix A= 2 -5 -4 has an eigenvalue 2 -4 -5 Two of the entries of A are replaced by I, y so that it will not be convenient to find the eigenvalues by an application. 5 An eigenvector of A corresponding to the eigenvalue is 1 Find the value of and enter your answer in the box below. X= Number (b) Suppose that characteristic equation of a 8 x 8 matrix M is (1 - 2)4...
(12) (7 marks) Let the distinct eigenvalues of a square matrix A be denoted by 11, ..., dk. Suppose the corresponding algebraic multiplicities are m1, ..., mk and that A is similar to an upper-triangular matrix. Show that k tr(A) = midi and det(A) = II (1;)" i=1 i=1
Find the eigenvalues of the given matrix. [-14 -6 36 16 1) A) -2.-4 B)-4 C)-2 D) -24 The characteristic polynomial of a 5 5 matrix is given below. Find the eigenvalues and their multiplicities 2) A5 - 24A4-189A3-486A2 2) A) 0 (multiplicity 2),-9 (multiplicity 2),-6 (multiplicity 1) B) 0 (multiplicity 1),9 (multiplicity 3), 6 (multiplicity ) C) 0 (multiplicity 2),9 (multiplicity 2),6 (multiplicity 1) D) 0 (multiplicity 2),-9 (multiplicity 2),6 (multiplicity 1) Diagonalize A- PDP-1 the matrix A, if...
Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal. -1 0-1 0-1 0 -107 Find the characteristic polynomial of A. far - 41 - Find the eigenvalues of A. (Enter your answers from smallest to largest.) (11, 12, 13) = Find the general form for every eigenvector corresponding to 11. (Uses as your parameter.) X1 = Find the general form for every eigenvector corresponding to 12. (Use t as your parameter.) x2 = (0.t,0)...