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Question 7 [10 points] For the matrix A below, find a value of k so that...
Question 10 [10 points] Find the basic eigenvectors of A corresponding to the eigenvalue . -3...
Question 10 [10 points] Find the basic eigenvectors of A corresponding to the eigenvalue . -3 0 0 1 A = 10 2 10 , i = -3 T0 0 -3| Number of Vectors: 1 Official Time: 15:57:24 SUBMIT AND MARK SAVE AND CLOSE
Question 7 [10 points) Find conditions on k that will make the matrix A invertible. To...
Question 7 [10 points) Find conditions on k that will make the matrix A invertible. To enter your answer first select 'always', never', or whether should be equal or not equal to specific values, then enter a value or a list of values separated by commas. k 0 2 A-8k-2 4 2-1 A is invertible: Always Always Never Question 8 [10 When k = Express the follow. When katrix A as a product of elementary matrices:
(1 point) Find the value of k for which the matrix -7 -7 A= 9 7...
(1 point) Find the value of k for which the matrix -7 -7 A= 9 7 -6 -6 3 -3 k has rank 2. k= -10
a) suppose that the nxn matrix A has its n eigenvalues arranged in decreasing order of absolute size, so that >>....
a) suppose that the nxn matrix A has its n eigenvalues arranged
in decreasing order of absolute size, so that >>....
each eigenvalue has its corresponding eigenvector, x1,x2,...,xn.
suppose we make some initial guess y(0) for an eigenvector.
suppose, too, that y(0) can be written in terms of the actual
eigenvectors in the form y(0)=alpha1.x1 +alpha2.x2
+...+alpha(n).x(n), where alpha1, alpha2, alpha(n) are constants.
by considering the "power method" type iteration y(k+1)=Ay(k) argue
that (see attached image)
b) from an nxn...
Question 14 [10 points] Given the following matrix A, find an invertible matrix U so that A is equal to UR, when R...
Question 14 [10 points] Given the following matrix A, find an invertible matrix U so that A is equal to UR, when R is the reduced row-echelon form of A: You can resize a matrix (when appropriate) by clicking and dragging the bottom right corner of the matrix. 5 -10 5 50 -15 A = 2 -3 1 17 -5 -1-24 7 -3 4 000 000 00 0
Question 14 [10 points] Given the following matrix A, find an invertible...
(1 point) Find the characteristic polynomial of the matrix 5 -5 A = 0 [ 5...
(1 point) Find the characteristic polynomial of the matrix 5 -5 A = 0 [ 5 -5 -2 5 0] 4. 0] p(x) = (1 point) Find the eigenvalues of the matrix [ 23 C = -9 1-9 -18 14 9 72 7 -36 : -31] The eigenvalues are (Enter your answers as a comma separated list. The list you enter should have repeated items if there are eigenvalues with multiplicity greater than one.) (1 point) Given that vi =...
please solve them clear Q1. Let A= be a 2 x 2 matrix. 45 (a) Find...
please solve them clear
Q1. Let A= be a 2 x 2 matrix. 45 (a) Find the characteristic polynomial of the matrix A. (5 pts) (b) Find all eigenvalues and associated eigenvectors of the matrix A. (10 pts) (c) If X is an eigenvalue of A, what do you think it would be the eigenvalue of the matrix 5A?(Justify your answer) (5 pts) Q2. Consider the matrix A = 2 -5 -6 1-50 (a) Find all eigenvalues of the matrix...
(8 points) [102] The matrix A= 0 3 0 (205 has a single real eigenvalue =...
(8 points) [102] The matrix A= 0 3 0 (205 has a single real eigenvalue = 3 with algebraic multiplicity three (a) Find a basis for the associated eigenspace. Basis = { (b) is the matrix A defective? A. A is not defective because the eigenvectors are linearly independent O B. A is defective because the geometric multiplicity of the eigenvalue is less than the algebraic multiplicity c. A is defective because it has only one eigenvalue D. A is...
Find all distinct eigenvalues of A. Then find the basic eigenvectors of A corresponding to each...
Find all distinct eigenvalues of A. Then find the basic eigenvectors of A corresponding to each eigenvalue. For each eigenvalue, specify the number of basic eigenvectors corresponding to that eigenvalue, then enter the eigenvalue followed by the basic eigenvectors corresponding to that eigenvalue. [o -6 -61 A = 0 -7 -6 10 4 3 Number of distinct eigenvalues: 1 Number of Vectors: 1 C
This assignment assesses the material covered in Modules 6-10. Write full and complete so- lutions, using...
This assignment assesses the material covered in Modules 6-10. Write full and complete so- lutions, using full sentences where appropriate. Explain all row operations when computing an RREF. Answer the questions asked. Questions 1-5 are worth 20 points each. The bonus question is worth 10 points (but points on this assignment are capped at 100). Recommended Deadline: April 24th Final Deadline: May 1st. 1. Compute the inverse of the matrix A = 1 3 1 4 -1 1 2 0...
Question 10 [10 points] Find the basic eigenvectors of A corresponding to the eigenvalue . -3 0 0 1 A = 10 2 10 , i = -3 T0 0 -3| Number of Vectors: 1 Official Time: 15:57:24 SUBMIT AND MARK SAVE AND CLOSE
Question 7 [10 points) Find conditions on k that will make the matrix A invertible. To enter your answer first select 'always', never', or whether should be equal or not equal to specific values, then enter a value or a list of values separated by commas. k 0 2 A-8k-2 4 2-1 A is invertible: Always Always Never Question 8 [10 When k = Express the follow. When katrix A as a product of elementary matrices:
(1 point) Find the value of k for which the matrix -7 -7 A= 9 7 -6 -6 3 -3 k has rank 2. k= -10
a) suppose that the nxn matrix A has its n eigenvalues arranged
in decreasing order of absolute size, so that >>....
each eigenvalue has its corresponding eigenvector, x1,x2,...,xn.
suppose we make some initial guess y(0) for an eigenvector.
suppose, too, that y(0) can be written in terms of the actual
eigenvectors in the form y(0)=alpha1.x1 +alpha2.x2
+...+alpha(n).x(n), where alpha1, alpha2, alpha(n) are constants.
by considering the "power method" type iteration y(k+1)=Ay(k) argue
that (see attached image)
b) from an nxn...
Question 14 [10 points] Given the following matrix A, find an invertible matrix U so that A is equal to UR, when R is the reduced row-echelon form of A: You can resize a matrix (when appropriate) by clicking and dragging the bottom right corner of the matrix. 5 -10 5 50 -15 A = 2 -3 1 17 -5 -1-24 7 -3 4 000 000 00 0
Question 14 [10 points] Given the following matrix A, find an invertible...
(1 point) Find the characteristic polynomial of the matrix 5 -5 A = 0 [ 5 -5 -2 5 0] 4. 0] p(x) = (1 point) Find the eigenvalues of the matrix [ 23 C = -9 1-9 -18 14 9 72 7 -36 : -31] The eigenvalues are (Enter your answers as a comma separated list. The list you enter should have repeated items if there are eigenvalues with multiplicity greater than one.) (1 point) Given that vi =...
please solve them clear
Q1. Let A= be a 2 x 2 matrix. 45 (a) Find the characteristic polynomial of the matrix A. (5 pts) (b) Find all eigenvalues and associated eigenvectors of the matrix A. (10 pts) (c) If X is an eigenvalue of A, what do you think it would be the eigenvalue of the matrix 5A?(Justify your answer) (5 pts) Q2. Consider the matrix A = 2 -5 -6 1-50 (a) Find all eigenvalues of the matrix...
(8 points) [102] The matrix A= 0 3 0 (205 has a single real eigenvalue = 3 with algebraic multiplicity three (a) Find a basis for the associated eigenspace. Basis = { (b) is the matrix A defective? A. A is not defective because the eigenvectors are linearly independent O B. A is defective because the geometric multiplicity of the eigenvalue is less than the algebraic multiplicity c. A is defective because it has only one eigenvalue D. A is...
Find all distinct eigenvalues of A. Then find the basic eigenvectors of A corresponding to each eigenvalue. For each eigenvalue, specify the number of basic eigenvectors corresponding to that eigenvalue, then enter the eigenvalue followed by the basic eigenvectors corresponding to that eigenvalue. [o -6 -61 A = 0 -7 -6 10 4 3 Number of distinct eigenvalues: 1 Number of Vectors: 1 C
This assignment assesses the material covered in Modules 6-10. Write full and complete so- lutions, using full sentences where appropriate. Explain all row operations when computing an RREF. Answer the questions asked. Questions 1-5 are worth 20 points each. The bonus question is worth 10 points (but points on this assignment are capped at 100). Recommended Deadline: April 24th Final Deadline: May 1st. 1. Compute the inverse of the matrix A = 1 3 1 4 -1 1 2 0...
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