Consider the matrix A=[acbd]. Assume that (a−d)2=−4bc(a−d)2=−4bc holds. Is AA always diagonalizable? If your answer is...
Consider the matrix
A=[acbd].
Assume that (a−d)2=−4bc(a−d)2=−4bc holds. Is AA always diagonalizable? If your answer is yes prove it. If your answer is no, give an example that shows AA is diagonalizable and give another example that shows AA is not diagonalizable.
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Consider the matrix
A=[acbd].
Assume that (a−d)2=−4bc(a−d)2=−4bc holds. Is AA always
diagonalizable? If your answer is...
Consider the matrica b d Assume llast (a.d = -4bc holds. is Ĥ always diagonalizable? If...
Consider the matrica b d Assume llast (a.d = -4bc holds. is Ĥ always diagonalizable? If your answer is yes prove it! If your answer no give an example that Shows example llhat show A is not diagonalizable A is diagonaligable and give another
(2) Consider the matrix (a) Find a value of x such that A is diagonalizable. (b)...
(2) Consider the matrix (a) Find a value of x such that A is diagonalizable. (b) Find a value of x such that A is not diagonalizable.
4. True/False.As always, give a brief explanation for your answer, if true, why true, or if...
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...
Bycalculatingthecharacteristicpolynomial,eigenvaluesanddimensionsoftheeigenspaces of each map or matrix below, determine if the given map or matrix is diagonalizable....
Bycalculatingthecharacteristicpolynomial,eigenvaluesanddimensionsoftheeigenspaces
of each map or matrix below, determine if the given map or matrix
is diagonalizable. If a map or matrix is diagonalizable,
diagonalize it （linear algebra)
1. By calculating the characteristic polynomial, eigenvalues and dimensions of the eigenspaces of each map or matrix below, determine if the given map or matrix is diagonalizable. If a map or matrix is diagonalizable, diagonalize it (that is, give a basis consisting of its eigenvectors) The field F over which you consider the...
Determine whether or not the given matrix A is diagonalizable. If it is, find a diagonalizing...
Determine whether or not the given matrix A is diagonalizable. If it is, find a diagonalizing matrix P and diagonal matrix D such that P-TAP =D 300 030 0 3 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 2 0 0 0 3 0 O A 0 1 0 The matrix is diagonalizable, (PD) = 0 0 1 1 0 3 (Use a comma to separate matrices as needed.) O...
Question 2. Give an example of the following, or if no example exists state that. As always, prove your answer in e...
Question 2. Give an example of the following, or if no example exists state that. As always, prove your answer in either case. (a) A finite non-normal extension of Q (b) A finite non-normal extension of R (c) A finite non-normal extension of F7
Question 2. Give an example of the following, or if no example exists state that. As always, prove your answer in either case. (a) A finite non-normal extension of Q (b) A finite non-normal extension of...
[1 2 37 1. Is the matrix 1 0 1 invertible? If yes, what is its...
[1 2 37 1. Is the matrix 1 0 1 invertible? If yes, what is its inverse? [O 2 -1 2. A matrix is called symmetric if At = A. What can you say about the shape of a symmetric matrix? Give an example of a symmetric matrix that is not a zero matrix. 3. A matrix is called anti-symmetric if A= -A. What can you say about the shape of an anti- symmetric matrix? Give an example of an...
4.(5 pts)Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and...
4.(5 pts)Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is diagonalizable. Show that it is, in fact, diagonalizable, and find C and D such that C (you may make this as trivial as you wish!) AC = D 5.(5 pts) Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is NOT diagonalizable. Show WHY it is not diagonalizable. 6. (5 pts) Let T:...
Show that the matrix is not diagonalizable. 2 43 0 21 0 03 STEP 1: Use...
Show that the matrix is not diagonalizable. 2 43 0 21 0 03 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) -- STEP 2: Find the eigenvectors x, and X corresponding to d, and 12, respectively, STEP 3: Since the matrix does not have Select linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
<Problem 2> Answer the following questions about the square matrix A of order 3: A= III....
<Problem 2> Answer the following questions about the square matrix A of order 3: A= III. The square matrix B of order 3 is diagonalizable and meets AB=BA. prove that any eigenvector p of A is also an eigenvector of B. IV. Find the square matrix B of order 3 that meets B2 = A, where B is diagonalizable and all eigenvalues of B are positive. V. The square matrix X of order 3 is diagonalizable and meets AX =...
Consider the matrica b d Assume llast (a.d = -4bc holds. is Ĥ always diagonalizable? If your answer is yes prove it! If your answer no give an example that Shows example llhat show A is not diagonalizable A is diagonaligable and give another
(2) Consider the matrix (a) Find a value of x such that A is diagonalizable. (b) Find a value of x such that A is not diagonalizable.
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...
Bycalculatingthecharacteristicpolynomial,eigenvaluesanddimensionsoftheeigenspaces
of each map or matrix below, determine if the given map or matrix
is diagonalizable. If a map or matrix is diagonalizable,
diagonalize it （linear algebra)
1. By calculating the characteristic polynomial, eigenvalues and dimensions of the eigenspaces of each map or matrix below, determine if the given map or matrix is diagonalizable. If a map or matrix is diagonalizable, diagonalize it (that is, give a basis consisting of its eigenvectors) The field F over which you consider the...
Determine whether or not the given matrix A is diagonalizable. If it is, find a diagonalizing matrix P and diagonal matrix D such that P-TAP =D 300 030 0 3 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 2 0 0 0 3 0 O A 0 1 0 The matrix is diagonalizable, (PD) = 0 0 1 1 0 3 (Use a comma to separate matrices as needed.) O...
Question 2. Give an example of the following, or if no example exists state that. As always, prove your answer in either case. (a) A finite non-normal extension of Q (b) A finite non-normal extension of R (c) A finite non-normal extension of F7
Question 2. Give an example of the following, or if no example exists state that. As always, prove your answer in either case. (a) A finite non-normal extension of Q (b) A finite non-normal extension of...
[1 2 37 1. Is the matrix 1 0 1 invertible? If yes, what is its inverse? [O 2 -1 2. A matrix is called symmetric if At = A. What can you say about the shape of a symmetric matrix? Give an example of a symmetric matrix that is not a zero matrix. 3. A matrix is called anti-symmetric if A= -A. What can you say about the shape of an anti- symmetric matrix? Give an example of an...
4.(5 pts)Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is diagonalizable. Show that it is, in fact, diagonalizable, and find C and D such that C (you may make this as trivial as you wish!) AC = D 5.(5 pts) Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is NOT diagonalizable. Show WHY it is not diagonalizable. 6. (5 pts) Let T:...
Show that the matrix is not diagonalizable. 2 43 0 21 0 03 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) -- STEP 2: Find the eigenvectors x, and X corresponding to d, and 12, respectively, STEP 3: Since the matrix does not have Select linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
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