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True or False: If A is an matrix that is both diagonalizable and invertible, then so...
Indicate whether the statement is true or false: If a matrix is invertible and diagonalizable, then its inverse is diagonalizable O O True False
-2 2 1 Determine if the matrix A = -4 4 2 is diagonalizable. If so, find an invertible matrix P and a 1 -1 0 diagonal matrix D such that A = PDP-1. If not, explain why.
4. True/False.As always, give a brief explanation for your answer, if true, why true, or if false what would make it true, or a counterexample - 2 pts each: a. If Spanv v, V}) = Span({w,W)= W , then W is 2-dimensional. b. The kernel of a linear transformation T: R8 -R5 cannot be trivial c. If A is an invertible matrix, then A is diagonalizable 0, then A cannot be full-rank d. If det(A) e. If A is an...
6. Suppose that A is a 3 3 diagonalizable matrix, so there is an invertible 3 x 3 matrix S and scalars a, b, c so that Let C1,C2, č3 be the columns of S. Use the equation S-1S - I3 to computeSč1, S-C2, S-1c3 Show that B[c1,c2,cs is an eigenbasis for A I3 to computeS-1a 6. Suppose that A is a 3 3 diagonalizable matrix, so there is an invertible 3 x 3 matrix S and scalars a, b,...
6. Suppose that A is a 3 3 diagonalizable matrix, so there is an invertible 3 x 3 matrix S and scalars a, b, c so that Let C1,C2, č3 be the columns of S. Use the equation S-1S - I3 to computeSč1, S-C2, S-1c3 Show that B[c1,c2,cs is an eigenbasis for A I3 to computeS-1a
True False a) For nxn A, A and AT can have different eigenvalues. b) The vector v 0 cannot be an eigenvector of A. c) If λ's an eigenvalue of A, then λ2 is an eigenvalue of A2. True False d) If A is invertible, then A is diagonalizable. e) If nxn A is singular, then Null(A) is an eigenspace of A. f) For nxn A, the product of the eigenvalues is the trace of A. True False g) If...
Indicate whether the statements are true or false (a) If A is orthogonally diagonalizable, then so is A2 (b) For any matrix A e Rmxn, AAT and AT A are symmetric matrices
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...
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...
Write true or false for each of the following statements. Provide justification for each answer—if true, give a brief explanation. If false, either provide a counterexample or contrast the statement with a similar true statement, explaining why the two cases differ. (5 points) If an nxn matrix A is diagonalizable then it has eigenvalues 11,...In with li #lj when i #j