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5. Consider the matrix A-1-6-7-3 Hint: The characteristic polynomial of A is p(λ ) =-(-2)0+ 1)2....
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...
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...
(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...
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...
o-point Point 43003 Consider the following (a) Compute the characteristic polynomial of A det(A - -...
o-point Point 43003 Consider the following (a) Compute the characteristic polynomial of A det(A - - (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 value) has eigenspace span has eigenspace span (largest A-value) (c) Compute the algebraic and geometric multiplicity of each eigenvalue. à has algebraic multiplicity and geometric multiplicity 2, has algebraic multiplicity and geometric multiplicity 2, has algebraic multiplicity and...
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. Consider the following matrix [1 0 -27 A=000 L-2 0 4] (a) (3 points) Find...
4. Consider the following matrix [1 0 -27 A=000 L-2 0 4] (a) (3 points) Find the characteristic polynomial of A. (b) (4 points) Find the eigenvalues of A. Give the algebraic multiplicity of each eigenvalue (c) (8 points) Find the eigenvectors corresponding to the eigenvalues found in part (b). (d) (4 points) Give a diagonal matrix D and an invertible matrix P such that A = PDP-1 (e) (6 points) Compute P-and verify that A= PDP- (show your steps).
1. Consider the matrix (a) Find the characteristic polynomial and eigenvalues of A (b) Find a...
1. Consider the matrix (a) Find the characteristic polynomial and eigenvalues of A (b) Find a basis for the eigenspace corresponding to each eigenvalue of A. (c) Find a diagonalization of A. That is, find an invertible matrix P and a diagonal matrix such that A - POP! (d) Use your diagonalization of A to compute A'. Simplify your answer.
(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...
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 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...
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...
(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...
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...
o-point Point 43003 Consider the following (a) Compute the characteristic polynomial of A det(A - - (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 value) has eigenspace span has eigenspace span (largest A-value) (c) Compute the algebraic and geometric multiplicity of each eigenvalue. à has algebraic multiplicity and geometric multiplicity 2, has algebraic multiplicity and geometric multiplicity 2, has algebraic multiplicity and...
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. Consider the following matrix [1 0 -27 A=000 L-2 0 4] (a) (3 points) Find the characteristic polynomial of A. (b) (4 points) Find the eigenvalues of A. Give the algebraic multiplicity of each eigenvalue (c) (8 points) Find the eigenvectors corresponding to the eigenvalues found in part (b). (d) (4 points) Give a diagonal matrix D and an invertible matrix P such that A = PDP-1 (e) (6 points) Compute P-and verify that A= PDP- (show your steps).
1. Consider the matrix (a) Find the characteristic polynomial and eigenvalues of A (b) Find a basis for the eigenspace corresponding to each eigenvalue of A. (c) Find a diagonalization of A. That is, find an invertible matrix P and a diagonal matrix such that A - POP! (d) Use your diagonalization of A to compute A'. Simplify your answer.
(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...
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)
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