Only a-c 8.3.2. Find the eigenvalues and a basis for the each of the eigenspaces of...
Problem 2: Let 4 1 2 5 1-1 0 3 2 0 3 2 a) Find the eigenvalues, eigenspaces of the linear operators LB, Lo. b) Using part a), find a basis for R3 that diagonalizes the linear operators c) Write B- EDE- with D a diagonal matrix. d) Find the eigenvalues, eigenspaces, and generalized eigenspaces of LA Problem 2: Let 4 1 2 5 1-1 0 3 2 0 3 2 a) Find the eigenvalues, eigenspaces of the linear...
Find a basis for the eigenspaces of matrix A. What is the algebraic and geometric multiplicities of its eigenvalues. Consider matrices 2 A= 2 -4 1 and -8 12 -2 3
1. Find the eigenvalues for the following matrices and bases for their corresponding eigenspaces. -28 10 (a) -75 27 -3 -4 6 (b) 8 12-18 4 5 -7 -17 5 5 (c) -40 13 10 -20 5 8
Matrix A is factored in the form PDP Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 1 1 1 2 2 1 2 4 2 2 8 5 0 0 A= 1 2 2 = 2 0-2 0 1 0 1 4 1 4 1 2 1 1 3 2 -1 0 0 0 1 1 8 3 1 4 Select the correct choice below and fill in the answer boxes to...
Consider the following. List the eigenvalues of A and bases of the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) has eigenspace span smallest 2-value has eigenspace span has eigenspace span largest 2-value A3= Determine whether A is diagonalizable. O Yes O No Find an invertible matrix P and a diagonal matrix D such that PAP = D. (Enter each matrix in the form [[row 1], [row 2], ..], where each row is a comma-separated list....
3. Find all the eigenvalues and corresponding eigenspaces for the matrix B = 4. Show that the matrix B = 0 1 is not diagonalizable. 0 4] Lo 5. Let 2, and 1, be two distinct eigenvalues of a matrix A (2, # 12). Assume V1, V2 are eigenvectors of A corresponding to 11 and 22 respectively. Prove that V1, V2 are linearly independent.
ees. For each eigenvalue, fins polynomial II Find the eigenvalues of the followin basis for the corresponding eigenspace. a. [6 - 24 - 4 2 -10 - 2 1 4 1 c. 3 1 0 1 To 3 1 Loo 3 e. -1 -1 10 ] f. [ -1-16 1-1-16 1 / -1 ol b. [ 7 -24 -61 2 -7 - lo 0 1 d. 3 -7 -41 -1 94 1 2 -14 -6 -5 51 0-4 -IC MINI...
Let the matrix 10 1 act on c. Find the eigenvalues and a basis for each eigenspace in c? 45 4 Select all that apply. 3+61 I A. 1 =7-61; v= A B. = -7 +61,v= -3-6i 15 6 -3-6 i O c. 1 = 7+6 iv= - 3+6 D. 1 = 7+61,v= 45 Click to select your answer(s). 10 1 Let the matrix act on c? Find the eigenvalues and a basis for each eigenspace in C? 45 4...
AB 31) Find the eigenvalues and eigenspaces of the matrix-4 0 4 Hint: One way to simplify 6 -2-3 a term of the form a +bi, where a and b are real numbers, is to multiply it by a -bi
5. Let (a) (2 marks) Find all eigenvalues of A (b) (4 marks) Find an orthonormal basis for each eigenspace of A (you may find an orthonormal basis by inspection or use the Gram-Schmidt algorithm on each eigenspace) (c) (2 marks) Deduce that A is orthogonally diagonalizable. Write down an orthogonal matrix P and a diagonal matrix D such that D P-AP. (d) (1 mark) Use the fact that P is an orthogonal matrix to find P-1 (e) (2 marks)...