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15. Use the characteristic equation to find the real eigenvalues of the following matrices. (a) [...
16. Diagonalize the following matrices if possible. (If not possible explain why not) Then compute A2....
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
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...
4(b) please 4. Find the characteristic polynomial, the eigenvalues and corresponding eigenvectors of each of the...
4(b) please
4. Find the characteristic polynomial, the eigenvalues and corresponding eigenvectors of each of the following matrices. 1 -2 3 1 2 (a (b) 2 6 6 2 1 13 3 -3 -5 -3 5. Diagonalize the matrix A = if possible. That is, find an invertible matrix P and 2 1 Inc.
Find the eigenvalues of the given matrix. [-14 -6 36 16 1) A) -2.-4 B)-4 C)-2...
Find the eigenvalues of the given matrix. [-14 -6 36 16 1) A) -2.-4 B)-4 C)-2 D) -24 The characteristic polynomial of a 5 5 matrix is given below. Find the eigenvalues and their multiplicities 2) A5 - 24A4-189A3-486A2 2) A) 0 (multiplicity 2),-9 (multiplicity 2),-6 (multiplicity 1) B) 0 (multiplicity 1),9 (multiplicity 3), 6 (multiplicity ) C) 0 (multiplicity 2),9 (multiplicity 2),6 (multiplicity 1) D) 0 (multiplicity 2),-9 (multiplicity 2),6 (multiplicity 1) Diagonalize A- PDP-1 the matrix A, if...
# 2: Consider the real symmetric matrix A= 4 1 a) What are the eigenvalues and...
# 2: Consider the real symmetric matrix A= 4 1 a) What are the eigenvalues and eigenvectors. [Hint: Use wolframalpha.] b) What is the trace of A, what is the sum of the eigenvalues of A. What is a general theorem th c) The eigenvalues of A are real. What is a general theorem which assert conditions that t d) Check that the eigenvectors are real. What is a general theorem which asserts conditions th asserts equality? eigenvalues are real...
3) (9 points) For each of the following matrices Find the eigenvalues and associated eigenvectors. If...
3) (9 points) For each of the following matrices Find the eigenvalues and associated eigenvectors. If possible, state the matrices P and D, such that A = PDP-1. (Hint: P is a matrix containing eigenvectors of A on its columns, and D is a diagonal matrix.) If it is not possible to find P and D, just state so. 11-133b a. A = 1 2 2 1-2 -2 -2 2 0 -1 3] b. A = [1 -4 110 0...
Question #25 Eigenv and Characteristic Equation, Eigenvalues, In Exercises 15-28, find (a) the characteristic eo and...
Question #25
Eigenv and Characteristic Equation, Eigenvalues, In Exercises 15-28, find (a) the characteristic eo and (b) the eigenvalues (and correspondinn of the matrix 15 uatias vect 1-4 6 -3 -2 1 -2 8 -2 4 18. L2 1 20. 0 3 2 1 2 2 -2 3 22. 0 0 21. 0 3-2 0 -1 2 3 2 3 24. 3 4 9 1 2 2 23.-2 5 2 -6 6-3 0 -3 5 25. -4 4 -10 26....
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...
(4) (15 marks) Repeat the Question 2 for the following matrices -3 4 0] 0 0...
(4) (15 marks) Repeat the Question 2 for the following matrices -3 4 0] 0 0 A -2 30 B 0 -1 0 -8 8 1 0 0 1 ū= 10 = > 3 (I) (2 mark) Find the characteristic polynomial of matrix A. (II) (1 mark) Find eigenvalues of the matrix A. III) (2 mark) Find a basis for the eigenspaces of matrix A. IV) (1 mark) What is the algebraic and geometric multiplicities of its eigenvalues. (V) (2...
Find the characteristic polynomial and the eigenvalues of the matrix. 3 1 -15 The characteristic polynomial...
Find the characteristic polynomial and the eigenvalues of the matrix. 3 1 -15 The characteristic polynomial is (Type an expression using à as the variable. Type an exact answer, using radicals as needed.) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The real eigenvalue(s) of the matrix is/are (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed. Type each answer only once.) OB. The...
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
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...
4(b) please
4. Find the characteristic polynomial, the eigenvalues and corresponding eigenvectors of each of the following matrices. 1 -2 3 1 2 (a (b) 2 6 6 2 1 13 3 -3 -5 -3 5. Diagonalize the matrix A = if possible. That is, find an invertible matrix P and 2 1 Inc.
Find the eigenvalues of the given matrix. [-14 -6 36 16 1) A) -2.-4 B)-4 C)-2 D) -24 The characteristic polynomial of a 5 5 matrix is given below. Find the eigenvalues and their multiplicities 2) A5 - 24A4-189A3-486A2 2) A) 0 (multiplicity 2),-9 (multiplicity 2),-6 (multiplicity 1) B) 0 (multiplicity 1),9 (multiplicity 3), 6 (multiplicity ) C) 0 (multiplicity 2),9 (multiplicity 2),6 (multiplicity 1) D) 0 (multiplicity 2),-9 (multiplicity 2),6 (multiplicity 1) Diagonalize A- PDP-1 the matrix A, if...
# 2: Consider the real symmetric matrix A= 4 1 a) What are the eigenvalues and eigenvectors. [Hint: Use wolframalpha.] b) What is the trace of A, what is the sum of the eigenvalues of A. What is a general theorem th c) The eigenvalues of A are real. What is a general theorem which assert conditions that t d) Check that the eigenvectors are real. What is a general theorem which asserts conditions th asserts equality? eigenvalues are real...
3) (9 points) For each of the following matrices Find the eigenvalues and associated eigenvectors. If possible, state the matrices P and D, such that A = PDP-1. (Hint: P is a matrix containing eigenvectors of A on its columns, and D is a diagonal matrix.) If it is not possible to find P and D, just state so. 11-133b a. A = 1 2 2 1-2 -2 -2 2 0 -1 3] b. A = [1 -4 110 0...
Question #25
Eigenv and Characteristic Equation, Eigenvalues, In Exercises 15-28, find (a) the characteristic eo and (b) the eigenvalues (and correspondinn of the matrix 15 uatias vect 1-4 6 -3 -2 1 -2 8 -2 4 18. L2 1 20. 0 3 2 1 2 2 -2 3 22. 0 0 21. 0 3-2 0 -1 2 3 2 3 24. 3 4 9 1 2 2 23.-2 5 2 -6 6-3 0 -3 5 25. -4 4 -10 26....
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...
(4) (15 marks) Repeat the Question 2 for the following matrices -3 4 0] 0 0 A -2 30 B 0 -1 0 -8 8 1 0 0 1 ū= 10 = > 3 (I) (2 mark) Find the characteristic polynomial of matrix A. (II) (1 mark) Find eigenvalues of the matrix A. III) (2 mark) Find a basis for the eigenspaces of matrix A. IV) (1 mark) What is the algebraic and geometric multiplicities of its eigenvalues. (V) (2...
Find the characteristic polynomial and the eigenvalues of the matrix. 3 1 -15 The characteristic polynomial is (Type an expression using à as the variable. Type an exact answer, using radicals as needed.) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The real eigenvalue(s) of the matrix is/are (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed. Type each answer only once.) OB. The...
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