2 (1 point) Show that A= 55 -3 1] 2 0 1 LO 03 and B= -3 9 | 12 0 6 -4 are similar matrices by finding an invertible matrix P satisfying 11] -4 A=P-1BP. P-1 =
point) Show that A57-133 24 56 and B 2 2 are similar matrices by finding an invertible matrix P satisfying A P-IBP. 30 72 3/30 72/3 point) Show that A57-133 24 56 and B 2 2 are similar matrices by finding an invertible matrix P satisfying A P-IBP. 30 72 3/30 72/3
1 A= 11 3 0 0 0 0 0 0 0 0 1 LO 0 0 0 ro 0 0 LO 1 1 0] 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 LO 0 0 C = 11 0 0 0 Which of the matrices below is the reduced row echelon matrix A. Matrix A and B B. Matrix A and C C. Matrix B and C D. All matrices...
Answer 7,8,9 1-11-1)--[-13.-(41-44)--:-- 3 1 0 0 -1 0 5 4 2-3 0 0 0 6. Consider the matrix A, above. Use diagonalization to evaluate A. 7. Consider the matrix B, above. Find a diagonal matrix D, and invertible matrix P, such that BPDP-1 8. Consider the matrix C, above. Find a diagonal matrix D, and invertible matrix P, such that C = PDP-1. If this is not possible, thus the matrix is not diagonalizable, explain why. 9. Consider the...
(1 point) A matrix A is said to be similar to a matrix B if there is an invertible matrix P such that B = PAP 1 Let A1, A2, and A3 be 3 x 3 matrices Prove that if A1 is similar to A2 and A2 is similar to A3, then A similar to A. Proof: Since A1 is similar to A2, for some invertible matrix P for some invertible matrix Q Since A2 is similar to A3 for...
13-15 please! 13. a 14. 15. 0 Find the eigenspaces of A = 0 1 -1 Then diagonalize A if you can. LO 0 1 b Determine values a, b, c for matrix A = 0 -2 c to be diagonalizable. LO 0 1) For nxn matrix A and B, true or false? a. A is diagonalizable if the sum of geometric multiplicities of the eigenvalues is n b. If A is invertible, the only real eigenvalues are 1 and...
Matrices A and B are called similar if there exists an invertible Matrix P such that: A= PBP^-1 Show that det(A) = det(B)
1-11 23 )--[-!?). - (111) DE 1 0 0 4 1 - 4 4 0-3 0 0 0 3 0 0 -1 0 5 4 2-3 E = 6. Consider the matrix A, above. Use diagonalization to evaluate A. 7. Consider the matrix B, above. Find a diagonal matrix D, and invertible matrix P, such that B = PDP- 8. Consider the matrix C, above. Find a diagonal matrix D, and invertible matrix P, such that C = PDP-!. If...
Two n x n matrices A and B are called similar if there is an invertible matrix P such that B = P-AP. Show that two similar matrices enjoy the following properties. (a) They have the same determinant. (b) They have the same eigenvalues: specifically, show that if v is an eigenvector of A with eigenvalue 1, then P-lv is an eigenvector of B with eigenvalue l. (c) For any polynomial p(x), P(A) = 0 is equivalent to p(B) =...
13 please 8. b. -2 3 0 0 0 0 -1 2 0 0-4 0 3 0-2 0 3 0 0 -2 0 3 0 4 o0-1 6 0 0 1 o 2 6 0 0 -1 6 10. For any positive integer k, prove that det(4t) - de(A)*. 11. Prove that if A is invertible, then den(A-1)- I/der(A) - det(4)- 12. We know in general that A-B丰B-A for two n x n matrices. However, prove that: det(A . B)-det(B...