Homework Answers
92 (a) The matrix A= 2 -5 -4 has an eigenvalue 2 -4 -5 Two of...
92 (a) The matrix A= 2 -5 -4 has an eigenvalue 2 -4 -5 Two of the entries of A are replaced by I, y so that it will not be convenient to find the eigenvalues by an application. 5 An eigenvector of A corresponding to the eigenvalue is 1 Find the value of and enter your answer in the box below. X= Number (b) Suppose that characteristic equation of a 8 x 8 matrix M is (1 - 2)4...
Let A be the matrix To 1 0] A= -4 4 0 1-2 0 1 (a)...
Let A be the matrix To 1 0] A= -4 4 0 1-2 0 1 (a) Find the eigenvalues and eigenvectors of A. (b) Find the algebraic multiplicity an, and the geometric multiplicity, g, of each eigenvalue. (c) For one of the eigenvalues you should have gi < az. (If not, redo the preceding parts!) Find a generalized eigenvector for this eigenvalue. (d) Verify that the eigenvectors and generalized eigenvectors are all linearly independent. (e) Find a fundamental set of...
7 -4 8 Consider the 3x3 matrix A= 4 -1 8 -4 4 - 5 (a)...
7 -4 8 Consider the 3x3 matrix A= 4 -1 8 -4 4 - 5 (a) Find the eigenvalues of A. Show every step of your work. The key to successful factorization is not to distribute anything in the determinant until you have factored out everything you possibly can from all terms. When your factorization is complete, it should show the algebraic multiplicity of each eigenvalue. (b) What is/are the eigenvector(s) corresponding to each eigenvalue? (c) What are the eigenspaces?
please help !!!! 10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a) Show that v = | 1 | and w = 1-2) are eigenvectors of A. b) Identify the defective eigenvalu...
please help !!!!
10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a) Show that v = | 1 | and w = 1-2) are eigenvectors of A. b) Identify the defective eigenvalue of A, and find a corresponding generalized eigenvector Ax c) Write out the general solution of x
10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a)...
Given system of equations. (1) Find all eigenvalues of the matrix (2) Choose an eigenvalue and...
Given system of equations. (1) Find all eigenvalues of the matrix (2) Choose an eigenvalue and find the corresponding eigenvector. (3) Find the general solution of the given system of equations.
is an eigenvalue invertible matrix with X as an eigenvalue. Show that of A-1. Suppose v...
is an eigenvalue invertible matrix with X as an eigenvalue. Show that of A-1. Suppose v ER is a nonzero column vector. Let A (a) Show that v is an eigenvector of A correspond zero column vector. Let A be the n xn matrix vvT. n eigenvector of A corresponding to eigenvalue = |v||2. lat O is an eigenvalue of multiplicity n - 1. (Hint: What is rank A?) (b) Show that 0 is an eigenvalue of
(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 =...
question about linear algebra 1 point) The matrix 16 0 -18 A 6 2 6 12 0-14 has λ =-2 as an eigenvalue with algebraic multiplicity 2, and λ = 4 as an eigenvalue with algebraic multiplicity 1. The eige...
question about linear algebra
1 point) The matrix 16 0 -18 A 6 2 6 12 0-14 has λ =-2 as an eigenvalue with algebraic multiplicity 2, and λ = 4 as an eigenvalue with algebraic multiplicity 1. The eigenvalue -2 has an associated eigenvector The eigenvalue 4 has an associated eigenvector
1 point) The matrix 16 0 -18 A 6 2 6 12 0-14 has λ =-2 as an eigenvalue with algebraic multiplicity 2, and λ = 4 as...
(1 point) The matrix. has an eigenvalue 1 of multiplicity 2 with corresponding eigenvector ü. Find...
(1 point) The matrix. has an eigenvalue 1 of multiplicity 2 with corresponding eigenvector ü. Find 1 and i. i = has an eigenvector ū =
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue...
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue 1. Let c be a scalar. Show that A-ch has eigenvector v, and corresponding eigenvalue X-c. (b) (8 marks) Let A = (33) i. Find the eigenvalues of A. ii. For one of the eigenvalues you have found, calculate the corresponding eigenvector. iii. Make use of part (a) to determine an eigenvalue and a corresponding eigenvector 2 2 of 5 - 1
92 (a) The matrix A= 2 -5 -4 has an eigenvalue 2 -4 -5 Two of the entries of A are replaced by I, y so that it will not be convenient to find the eigenvalues by an application. 5 An eigenvector of A corresponding to the eigenvalue is 1 Find the value of and enter your answer in the box below. X= Number (b) Suppose that characteristic equation of a 8 x 8 matrix M is (1 - 2)4...
Let A be the matrix To 1 0] A= -4 4 0 1-2 0 1 (a) Find the eigenvalues and eigenvectors of A. (b) Find the algebraic multiplicity an, and the geometric multiplicity, g, of each eigenvalue. (c) For one of the eigenvalues you should have gi < az. (If not, redo the preceding parts!) Find a generalized eigenvector for this eigenvalue. (d) Verify that the eigenvectors and generalized eigenvectors are all linearly independent. (e) Find a fundamental set of...
7 -4 8 Consider the 3x3 matrix A= 4 -1 8 -4 4 - 5 (a) Find the eigenvalues of A. Show every step of your work. The key to successful factorization is not to distribute anything in the determinant until you have factored out everything you possibly can from all terms. When your factorization is complete, it should show the algebraic multiplicity of each eigenvalue. (b) What is/are the eigenvector(s) corresponding to each eigenvalue? (c) What are the eigenspaces?
please help !!!!
10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a) Show that v = | 1 | and w = 1-2) are eigenvectors of A. b) Identify the defective eigenvalue of A, and find a corresponding generalized eigenvector Ax c) Write out the general solution of x
10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a)...
Given system of equations. (1) Find all eigenvalues of the matrix (2) Choose an eigenvalue and find the corresponding eigenvector. (3) Find the general solution of the given system of equations.
is an eigenvalue invertible matrix with X as an eigenvalue. Show that of A-1. Suppose v ER is a nonzero column vector. Let A (a) Show that v is an eigenvector of A correspond zero column vector. Let A be the n xn matrix vvT. n eigenvector of A corresponding to eigenvalue = |v||2. lat O is an eigenvalue of multiplicity n - 1. (Hint: What is rank A?) (b) Show that 0 is an eigenvalue of
(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 =...
question about linear algebra
1 point) The matrix 16 0 -18 A 6 2 6 12 0-14 has λ =-2 as an eigenvalue with algebraic multiplicity 2, and λ = 4 as an eigenvalue with algebraic multiplicity 1. The eigenvalue -2 has an associated eigenvector The eigenvalue 4 has an associated eigenvector
1 point) The matrix 16 0 -18 A 6 2 6 12 0-14 has λ =-2 as an eigenvalue with algebraic multiplicity 2, and λ = 4 as...
(1 point) The matrix. has an eigenvalue 1 of multiplicity 2 with corresponding eigenvector ü. Find 1 and i. i = has an eigenvector ū =
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue 1. Let c be a scalar. Show that A-ch has eigenvector v, and corresponding eigenvalue X-c. (b) (8 marks) Let A = (33) i. Find the eigenvalues of A. ii. For one of the eigenvalues you have found, calculate the corresponding eigenvector. iii. Make use of part (a) to determine an eigenvalue and a corresponding eigenvector 2 2 of 5 - 1
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