Homework Answers
Algebric Multiplicity is that
how much time eigen value of matrix repeat.And geometric
multiplicity always greather then equal to 1 and less then equal to
algebric multiplicity.so algebric and geometric multiplicity for
each eigen value is one.
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o-point Point 43003 Consider the following (a) Compute the characteristic polynomial of A det(A - -...
Consider the following A= 0-51 0 0 6 (a) Compute the characteristic polynomial of A det(A...
Consider the following A= 0-51 0 0 6 (a) Compute the characteristic polynomial of A det(A - Ar)0 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) has eigenspace span (smallest A-value) has eigenspace span has eigenspace span (largest A-value) (c) Compute the algebraic and geometric multiplicity of each eigenvalue 1 has algebraic multiplicity i2 has algebraic multiplicity 3 has algebraic multiplicity X and geometric multiplicity 1...
O 1/13 points | Previous Answers poolelinalg4 4.3.003.nva 5. Consider the following. 1 0 0-3 1...
O 1/13 points | Previous Answers poolelinalg4 4.3.003.nva 5. Consider the following. 1 0 0-3 1 A= 0 4 0 (a) Compute the characteristic polynomial of A. det(A- λ- (1-λ) (-3- λ ) (4- λ ) (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (F λι- has eigenspace span (small λ has eigenspace span has eigenspace span (largestA 41 (c) Compute the algebraic and geometric multiplicity of each eigenvalue. has algebraic multiplicity 2 has algebraic multiplicity...
4 0 5 A 6-1 6 L5 0 4 (a) Compute the characteristic polynomial of A....
4 0 5 A 6-1 6 L5 0 4 (a) Compute the characteristic polynomial of A. det(A - A) - (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) λι ] has eigenspace span "L (smallest λ-value) has eigenspace span has eigenspace span (largest λ-value)
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...
3. (a) For the following matrix A, compute the characteristic polynomial C(A) = det(A ?): A-1...
3. (a) For the following matrix A, compute the characteristic polynomial C(A) = det(A ?): A-1 1 (b) Find all eigenvalues of A, using the following additional information: This miatrix has exactly 2 eigenvalues. We denote these ??,A2, where ?1 < ?2. . Each Xi is an integer, and satisfies-2 < ?? 2. (c) Given an eigenvalue ?? of A, we define the corresponding eigenspace to be the nullspace of A-?,I; note that this consists of all eigenvectors corresponding to...
Consider the following. List the eigenvalues of A and bases of the corresponding eigenspaces. (Repeated eigenvalues...
Consider the following. List the eigenvalues of A and bases of the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) has eigenspace span smallest 2-value has eigenspace span has eigenspace span largest 2-value A3= Determine whether A is diagonalizable. O Yes O No Find an invertible matrix P and a diagonal matrix D such that PAP = D. (Enter each matrix in the form [[row 1], [row 2], ..], where each row is a comma-separated list....
2. (-16 Points) DETAILS CHENEYLINALG2 6.1.017. 0/2 Submissions Used 9 Let A - Find the characteristic...
2. (-16 Points) DETAILS CHENEYLINALG2 6.1.017. 0/2 Submissions Used 9 Let A - Find the characteristic polynomial. 11 Det(A - AI) - Find the eigenvalues and eigenvectors for each eigenvalue. (Order your answers from smallest to largest eigenvalue.) 21 has eigenspace span 12 has eigenspace span Find a matrix P such that p-'AP is a diagonal matrix. P
(1 point) The linear transformation T: R4 R4 below is diagonalizable. T(x,y,z,w) = (x – -...
(1 point) The linear transformation T: R4 R4 below is diagonalizable. T(x,y,z,w) = (x – - (2x + y), -z, 2 – 3w Compute the following. (Click to open and close sections below). (A) Characteristic Polynomial Compute the characteristic polynomial (as a function of t). A(t) = (B) Roots and Multiplicities Find the roots of A(t) and their algebraic multiplicities. Root Multiplicity t= t= t= t= (Leave any unneeded answer spaces blank.) (C) Eigenvalues and Eigenspaces Find the eigenvalues and...
13. -14 points PoolelinAlg4 4.1.027. Find all of the eigenvalues of the matrix A over the...
13. -14 points PoolelinAlg4 4.1.027. Find all of the eigenvalues of the matrix A over the complex numbers C. Give bases for each of the corresponding eigenspaces. 1-C has eigenspace span has elgenspace (-value with smaller imaginary part) 12 - has eigenspace span (-value with larger imaginary part) Need Help? Read It Talk to a Tutor 14. + -14 points PooleLinAlg4 4.1.030. Find all of the eigenvalues of the matrix A over the complex numbers C. Give bases for each...
Let A be a square matrix with eigenvalue λ and corresponding eigenvector x. Annment 5 Caure...
Let A be a square matrix with eigenvalue λ and
corresponding eigenvector x.
Annment 5 Caure MATH 1 x CGet Homewarcx Enenvalue and CAcademic famxG lgeb rair mulbip Redured Rew F x Ga print sereenx CLat A BeA Su Agebrair and G Shep-hy-Step Ca x x x C https/www.webessignnet/MwebyStudent/Assignment-Responses/submit7dep-21389386 (b) Let A be a squara matrix with eigenvalue a and comasponding aigenvector x a. For any positive integer n, " is an eigenvalue of A" with corresponding eigenvector x b....
Consider the following A= 0-51 0 0 6 (a) Compute the characteristic polynomial of A det(A - Ar)0 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) has eigenspace span (smallest A-value) has eigenspace span has eigenspace span (largest A-value) (c) Compute the algebraic and geometric multiplicity of each eigenvalue 1 has algebraic multiplicity i2 has algebraic multiplicity 3 has algebraic multiplicity X and geometric multiplicity 1...
O 1/13 points | Previous Answers poolelinalg4 4.3.003.nva 5. Consider the following. 1 0 0-3 1 A= 0 4 0 (a) Compute the characteristic polynomial of A. det(A- λ- (1-λ) (-3- λ ) (4- λ ) (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (F λι- has eigenspace span (small λ has eigenspace span has eigenspace span (largestA 41 (c) Compute the algebraic and geometric multiplicity of each eigenvalue. has algebraic multiplicity 2 has algebraic multiplicity...
4 0 5 A 6-1 6 L5 0 4 (a) Compute the characteristic polynomial of A. det(A - A) - (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) λι ] has eigenspace span "L (smallest λ-value) has eigenspace span has eigenspace span (largest λ-value)
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...
3. (a) For the following matrix A, compute the characteristic polynomial C(A) = det(A ?): A-1 1 (b) Find all eigenvalues of A, using the following additional information: This miatrix has exactly 2 eigenvalues. We denote these ??,A2, where ?1 < ?2. . Each Xi is an integer, and satisfies-2 < ?? 2. (c) Given an eigenvalue ?? of A, we define the corresponding eigenspace to be the nullspace of A-?,I; note that this consists of all eigenvectors corresponding to...
Consider the following. List the eigenvalues of A and bases of the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) has eigenspace span smallest 2-value has eigenspace span has eigenspace span largest 2-value A3= Determine whether A is diagonalizable. O Yes O No Find an invertible matrix P and a diagonal matrix D such that PAP = D. (Enter each matrix in the form [[row 1], [row 2], ..], where each row is a comma-separated list....
2. (-16 Points) DETAILS CHENEYLINALG2 6.1.017. 0/2 Submissions Used 9 Let A - Find the characteristic polynomial. 11 Det(A - AI) - Find the eigenvalues and eigenvectors for each eigenvalue. (Order your answers from smallest to largest eigenvalue.) 21 has eigenspace span 12 has eigenspace span Find a matrix P such that p-'AP is a diagonal matrix. P
(1 point) The linear transformation T: R4 R4 below is diagonalizable. T(x,y,z,w) = (x – - (2x + y), -z, 2 – 3w Compute the following. (Click to open and close sections below). (A) Characteristic Polynomial Compute the characteristic polynomial (as a function of t). A(t) = (B) Roots and Multiplicities Find the roots of A(t) and their algebraic multiplicities. Root Multiplicity t= t= t= t= (Leave any unneeded answer spaces blank.) (C) Eigenvalues and Eigenspaces Find the eigenvalues and...
13. -14 points PoolelinAlg4 4.1.027. Find all of the eigenvalues of the matrix A over the complex numbers C. Give bases for each of the corresponding eigenspaces. 1-C has eigenspace span has elgenspace (-value with smaller imaginary part) 12 - has eigenspace span (-value with larger imaginary part) Need Help? Read It Talk to a Tutor 14. + -14 points PooleLinAlg4 4.1.030. Find all of the eigenvalues of the matrix A over the complex numbers C. Give bases for each...
Let A be a square matrix with eigenvalue λ and
corresponding eigenvector x.
Annment 5 Caure MATH 1 x CGet Homewarcx Enenvalue and CAcademic famxG lgeb rair mulbip Redured Rew F x Ga print sereenx CLat A BeA Su Agebrair and G Shep-hy-Step Ca x x x C https/www.webessignnet/MwebyStudent/Assignment-Responses/submit7dep-21389386 (b) Let A be a squara matrix with eigenvalue a and comasponding aigenvector x a. For any positive integer n, " is an eigenvalue of A" with corresponding eigenvector x b....
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