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3 For each of the matrices below: (i) Find the characteristic polynomial (ii) Determine the eigenvalues...
(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...
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...
Find the characteristic polynomial of matrix A. (II) Find eigenvalues of the matrix A. Consider matrices...
Find the characteristic polynomial of matrix A.
(II) Find eigenvalues of the matrix A.
Consider matrices 2 A= 2 -4 1 and -8 12 -2 3
5. Consider the matrix A-1-6-7-3 Hint: The characteristic polynomial of A is p(λ ) =-(-2)0+ 1)2....
5. Consider the matrix A-1-6-7-3 Hint: The characteristic polynomial of A is p(λ ) =-(-2)0+ 1)2. (a) Find the eigenvalues of A and bases for the corresponding eigenspaces. (b) Determine the geometric and algebraic multiplicities of each eigenvalue and whether A is diagonalizable or not. If it is, give a diagonal matrix D and an invertible matrix S such that A-SDS-1. If it's not, say why not.
(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...
1. Consider the matrix A= 1 3 -3 (a) Find the characteristic polynomial and eigenvalues of...
1. Consider the matrix A= 1 3 -3 (a) Find the characteristic polynomial and eigenvalues of A. (b) Find a basis for the eigenspace corresponding to each eigenvalue of A.
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.
Question 1: Question 2: Thx, will give a thumb Determine the algebraic and geometric multiplicity of...
Question 1:
Question 2:
Thx, will give a thumb
Determine the algebraic and geometric multiplicity of each eigenvalue of the matrix. 2 3 3 3 2 3 3 3 2 Identify the eigenvalue(s). Select the correct choice below and fill in the answer box(es) to complete your choice. O A. There is one distinct eigenvalue, 1 = OB. There are two distinct eigenvalues, hy and 12 (Use ascending order.) OC. There are three distinct eigenvalues, 14 , 22 = (Use...
Determine the algebraic and geometric multiplicities of the eigenvalues for the following matrix. B = 13...
Determine the algebraic and geometric multiplicities of the eigenvalues for the following matrix. B = 13 71 has characteristic equation (3-1)(6 - 1) = 0 LO 6] First determine the eigenvalues, order them from smallest to greatest: 11 = 12 = Now determine the algebraic and geometric multiplicities for each eigenvalue above. You can do this with direct computation or using any of the theorems discussed in class to avoid computation. ab(11) = YB(11) = ab(12) = YB(12) = We...
15. Use the characteristic equation to find the real eigenvalues of the following matrices. (a) [...
15. Use the characteristic equation to find the real eigenvalues of the following matrices. (a) [ ] 6 (b) | 9 -9 -6 -9 6 -6 3 1 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= 10 -1 15 3 -9 2=4 -2 10)
(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...
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...
Find the characteristic polynomial of matrix A.
(II) Find eigenvalues of the matrix A.
Consider matrices 2 A= 2 -4 1 and -8 12 -2 3
5. Consider the matrix A-1-6-7-3 Hint: The characteristic polynomial of A is p(λ ) =-(-2)0+ 1)2. (a) Find the eigenvalues of A and bases for the corresponding eigenspaces. (b) Determine the geometric and algebraic multiplicities of each eigenvalue and whether A is diagonalizable or not. If it is, give a diagonal matrix D and an invertible matrix S such that A-SDS-1. If it's not, say why not.
(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...
1. Consider the matrix A= 1 3 -3 (a) Find the characteristic polynomial and eigenvalues of A. (b) Find a basis for the eigenspace corresponding to each eigenvalue of A.
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.
Question 1:
Question 2:
Thx, will give a thumb
Determine the algebraic and geometric multiplicity of each eigenvalue of the matrix. 2 3 3 3 2 3 3 3 2 Identify the eigenvalue(s). Select the correct choice below and fill in the answer box(es) to complete your choice. O A. There is one distinct eigenvalue, 1 = OB. There are two distinct eigenvalues, hy and 12 (Use ascending order.) OC. There are three distinct eigenvalues, 14 , 22 = (Use...
Determine the algebraic and geometric multiplicities of the eigenvalues for the following matrix. B = 13 71 has characteristic equation (3-1)(6 - 1) = 0 LO 6] First determine the eigenvalues, order them from smallest to greatest: 11 = 12 = Now determine the algebraic and geometric multiplicities for each eigenvalue above. You can do this with direct computation or using any of the theorems discussed in class to avoid computation. ab(11) = YB(11) = ab(12) = YB(12) = We...
15. Use the characteristic equation to find the real eigenvalues of the following matrices. (a) [ ] 6 (b) | 9 -9 -6 -9 6 -6 3 1 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= 10 -1 15 3 -9 2=4 -2 10)
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