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For each of the following matrices, determine if A is diagonalizable. If it is, find a matrix S and a matrix B such that A = SBS-1. You do not need to compute S1. Then find a matrix similar to A3000...
We say that A and B are similar matrices if A = SBS-1 for some invertible...
We say that A and B are similar matrices if A = SBS-1 for some invertible matrix S. Are the following true or false. Given a mathematical reason (proof). (a) If A and B are similar, then A and B have the same eigenvalues. Answer: (b) If A and B are similar, then A and B have the same eigenvectors. Answer: c) If A and B are similar, then A - 51 and B – 51 are similar. Answer: (d)...
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...
6. For each of the following matrices A solve the eigenvalue problem. If A is diagonalizable,...
6. For each of the following matrices A solve the eigenvalue problem. If A is diagonalizable, find a matrix P that diagonalizes A by a similarity transformation D-PlAP and the respective diagonal matrix D. If A is not diagonalizable, briefly explain why -1 4 2 (d) A-|-| 3 1 -1 2 2 -1 0 1 6 3 (a) A- (b)As|0 1 0| (c) A-1-3 0 11 -4 0 3
2. For the following matrices, find a matrix Pthat diagonalizes A and compute p-'AP. If the...
2. For the following matrices, find a matrix Pthat diagonalizes A and compute p-'AP. If the matrix is not diagonalizable, say so and give a reason why. -14 12 (a) A= -2017 100 (b) A011 011
Are the two matrices similar? If so, find a matrix P such that B = p-1AP....
Are the two matrices similar? If so, find a matrix P such that B = p-1AP. (If not possible, enter IMPOSSIBLE.) 200 100 B = A= 0 3 0 03 0 0 0 1 0 0 2 0 0 ра 0 11 X
(60) Determine if (1 - ) is diagonalizable. You do not need to compuſes and D....
(60) Determine if (1 - ) is diagonalizable. You do not need to compuſes and D. You just need to determine if it is diagonalizable or not (and give a clear argument as to why“). (62) Compute all the values for a and b for which (a ] is nondefective (7a) Compute the Wronskian of the functions y; = 1, y = x, y3 = x?
15. Use the characteristic equation to find the real eigenvalues of the following matrices. (a) [...
15. Use the characteristic equation to find the real eigenvalues of the following matrices. (a) [ ] 6 (b) | 9 -9 -6 -9 6 -6 3 1 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= 10 -1 15 3 -9 2=4 -2 10)
3 For each of the matrices below: (i) Find the characteristic polynomial (ii) Determine the eigenvalues...
3 For each of the matrices below: (i) Find the characteristic polynomial (ii) Determine the eigenvalues (ii Find a basis for each eigenspace (iv) Find the algebraic and geometric multiplicities of the eigenvalues (v) Determine if the matrix is diagonalizable, and if it is, diagonalize it. -2 3 (a) A -3 2
3 For each of the matrices below: (i) Find the characteristic polynomial (ii) Determine the eigenvalues (ii Find a basis for each eigenspace (iv) Find the algebraic and...
1 Compute and completely factor the characteristic polynomial of the following matrix: 0 A= -4 5...
1 Compute and completely factor the characteristic polynomial of the following matrix: 0 A= -4 5 0 1 1 For credit, you have to factor the polynomial and show work for each step. B In the following, use complex numbers if necessary. For each of the following matrices: • compute the characteristic polynomial; • list all the eigenvalues (possibly complex) with their algebraic multiplicity; • for each eigenvalue, find a basis (possibly complex) of the corresponding eigenspace, and write the...
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...
We say that A and B are similar matrices if A = SBS-1 for some invertible matrix S. Are the following true or false. Given a mathematical reason (proof). (a) If A and B are similar, then A and B have the same eigenvalues. Answer: (b) If A and B are similar, then A and B have the same eigenvectors. Answer: c) If A and B are similar, then A - 51 and B – 51 are similar. Answer: (d)...
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...
6. For each of the following matrices A solve the eigenvalue problem. If A is diagonalizable, find a matrix P that diagonalizes A by a similarity transformation D-PlAP and the respective diagonal matrix D. If A is not diagonalizable, briefly explain why -1 4 2 (d) A-|-| 3 1 -1 2 2 -1 0 1 6 3 (a) A- (b)As|0 1 0| (c) A-1-3 0 11 -4 0 3
2. For the following matrices, find a matrix Pthat diagonalizes A and compute p-'AP. If the matrix is not diagonalizable, say so and give a reason why. -14 12 (a) A= -2017 100 (b) A011 011
Are the two matrices similar? If so, find a matrix P such that B = p-1AP. (If not possible, enter IMPOSSIBLE.) 200 100 B = A= 0 3 0 03 0 0 0 1 0 0 2 0 0 ра 0 11 X
(60) Determine if (1 - ) is diagonalizable. You do not need to compuſes and D. You just need to determine if it is diagonalizable or not (and give a clear argument as to why“). (62) Compute all the values for a and b for which (a ] is nondefective (7a) Compute the Wronskian of the functions y; = 1, y = x, y3 = x?
15. Use the characteristic equation to find the real eigenvalues of the following matrices. (a) [ ] 6 (b) | 9 -9 -6 -9 6 -6 3 1 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= 10 -1 15 3 -9 2=4 -2 10)
3 For each of the matrices below: (i) Find the characteristic polynomial (ii) Determine the eigenvalues (ii Find a basis for each eigenspace (iv) Find the algebraic and geometric multiplicities of the eigenvalues (v) Determine if the matrix is diagonalizable, and if it is, diagonalize it. -2 3 (a) A -3 2
3 For each of the matrices below: (i) Find the characteristic polynomial (ii) Determine the eigenvalues (ii Find a basis for each eigenspace (iv) Find the algebraic and...
1 Compute and completely factor the characteristic polynomial of the following matrix: 0 A= -4 5 0 1 1 For credit, you have to factor the polynomial and show work for each step. B In the following, use complex numbers if necessary. For each of the following matrices: • compute the characteristic polynomial; • list all the eigenvalues (possibly complex) with their algebraic multiplicity; • for each eigenvalue, find a basis (possibly complex) of the corresponding eigenspace, and write the...
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...
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