e Diagonalize the matrices and compute A and B10. 「3000 2 2 A=1141| and B=10200 1 0 0 3 e Diagonalize the matrice...
1. Orthogonally diagonalize the following matrices, if possible. If it is possi- on of the matrix ble, give the spectral decompositi 0-3 0 2 1. Orthogonally diagonalize the following matrices, if possible. If it is possi- on of the matrix ble, give the spectral decompositi 0-3 0 2
7 3. Diagonalize A = 1 0 0 0 . Use this diagonalization to compute A". 15 -2)
7 -1 -1 3. Diagonalize A = 0 0 Use this diagonalization to compute A". 15 -2
16. Diagonalize the following matrices if possible. (If not possible explain why not) Then compute A2. (Use the diagonal matrix to do the computation if A was diagonalizable) One of the Eigen-values is provided to get you started. A= [-2 3 1-9 10 -1 15 4 -2 10. 2=4
Diagonalize a. b. c. d. e. f. Diagonalize A A = 1 3 4 2 a. A = PDP-1 b. A = PDP-1 1 Р 1 1 OC. A = PDP-1 -1 3 P = 2 5 d. A = PDP-1 -3 1 P= -4 1 e. A = PDP-1 1 -1 P 3 1 Of A = PDP-1 P-[31] -- [6-2] [37] - [64] P=[ +3 z] --[: = D = 10 03
2. (14pts) Diagonalize the following matrices, B = [ 4 1 1 1] 1 4 1 1 A= 1 1 4 1 1 1 1 4 Find formulas for Ak, Bk, k > 1. [ 4 0 | 0 4 0 0 | 1 0 0 0 1 0 0 2 0 0 2
Problem 5 Diagonalize B and compute XA*X-1 to prove this formula for Be, (sections 6.1, 6.2) Bk=15+ 5+-4k has 0 41, Compute also , end sin 0 4 Problem 5 Diagonalize B and compute XA*X-1 to prove this formula for Be, (sections 6.1, 6.2) Bk=15+ 5+-4k has 0 41, Compute also , end sin 0 4
2 0 -21 3. Let A= 1 3 2 LO 0 3 (a) Find the characteristic equation of A. in Find the other (b) One of the eigenvalues for A is ) = 2 with corresponding eigenvector 1 10 eigenvalue and a basis for the eigenspace associated to it. (e) Find matrices S and B that diagonalize A, if possible.
If A and B are 3x3 matrices and A = 1, |B 3, compute the determinant If A and B are 3x3 matrices and A = 1, |B 3, compute the determinant
5. Suppose A, B are 2 × 2 matrices, such that 1 -3 (a) Compute (AB)-1 Answer: (b) Compute (A)-1 Answer: