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![7 olet A=To ] Characteristic polynomial of A: Pas 10 Hal = (1-0)? = 1-22+72 [The algebraic multiplicity of of A is the number](http://img.homeworklib.com/questions/d19ad120-240a-11eb-94ce-233dd6e541bc.png?x-oss-process=image/resize,w_560)
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1 1 1 Find the algebraic and geometric multiplicity of the...
Q1 Existence 5 Points Every square matrix has at least one eigenvalue. O True O False...
Q1 Existence 5 Points Every square matrix has at least one eigenvalue. O True O False Save Answer Q2 Basis 5 Points Let A be an (n xn) matrix, and assume that A has n different eigenvalues, then there is a basis of R" consisting eigenvectors of A. O False O True Q3 Computation 5 Points [ 1 Find the algebraic and geometric multiplicity of the unique eigenvalue of 1 1 Write your answer in the form [a, g] where...
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...
For the given Matrix B, find: 1. The algebraic multiplicity of each eigenvalue. 2. The geometric...
For the given Matrix B, find: 1. The algebraic multiplicity of each eigenvalue. 2. The geometric multiplicity of each eigenvalue. 3. The matrix B is it Diagonalizable? If YES, provide the matrices P and D. ( 22-1 B = 1 3 -1 (-1 -2 2
Find a basis for each eigenspace and calculate the geometric multiplicity of each eigenvalue. 3 2...
Find a basis for each eigenspace and calculate the geometric multiplicity of each eigenvalue. 3 2 The matrix A = 0 2 0 has eigenvalues X1 = 2 and X2 1 2 3 For each eigenvalue di, use the rank-nullity theorem to calculate the geometric multiplicity dim(Ex). Find the eigenvalues of A = 0 0 -1 0 0 geometric multiplicity of each eigenvalue. -7- Calculate the algebraic and
1. The symmetric matrix [4 1 1 1 A = 4-1 1 -1 4 -1 4 -1 has eigenvalues A = 1 (with algebraic multiplicity 1) and A...
1. The symmetric matrix [4 1 1 1 A = 4-1 1 -1 4 -1 4 -1 has eigenvalues A = 1 (with algebraic multiplicity 1) and A 5 (with algebraic multiplicity 3). a) Find bases for the eigenspaces E(1) and E(5). b) Apply the Gram-Schmidt process to your basis for E(5) to find an onal basis for E (5) orthog- (c) Hence write down an that QT AQ = D. orthogonal matrix Q and a diagonal matrix D such...
Problem 6: (multiplicity) atrices given below, statethe einenvalus of the matieace, ox to do this one and give the algebraic and geometric multiplic ities of each. For each eigenvalue, give a basis f...
Problem 6: (multiplicity) atrices given below, statethe einenvalus of the matieace, ox to do this one and give the algebraic and geometric multiplic ities of each. For each eigenvalue, give a basis for the eigenspace. OK to do this one ompletely in Octave, but be sure to interpret the answers it gives you (show tiny numbers like 1D-16 as zeros, and be sure to discard duplicate basis vectors) 4 0 0 0 0 0 4 0 0 0 A-2 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...
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...
Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric...
Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval [0, 21). Round your answer to four decimal places, if necessary. If there is no solution, indicate "No Solution." V3tan(x) + 1 = 0 Answer How to enter your answer Keypad Keyboard Shortcuts Enter your answer in radians, as an exact answer when possible. Multiple solutions should be separated by commas. Selecting a radio button will replace the entered answer...
Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric...
Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval [0, 21). Round your answer to four decimal places, if necessary. If there is no solution, indicate "No Solution." cot(-x) = -2cot(x) – 5 Answer How to enter your answer Keypad Keyboard Shortcuts Enter your answer in radians, as an exact answer when possible. Multiple solutions should be separated by commas. Selecting a radio button will replace the entered answer...
Q1 Existence 5 Points Every square matrix has at least one eigenvalue. O True O False Save Answer Q2 Basis 5 Points Let A be an (n xn) matrix, and assume that A has n different eigenvalues, then there is a basis of R" consisting eigenvectors of A. O False O True Q3 Computation 5 Points [ 1 Find the algebraic and geometric multiplicity of the unique eigenvalue of 1 1 Write your answer in the form [a, g] where...
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...
For the given Matrix B, find: 1. The algebraic multiplicity of each eigenvalue. 2. The geometric multiplicity of each eigenvalue. 3. The matrix B is it Diagonalizable? If YES, provide the matrices P and D. ( 22-1 B = 1 3 -1 (-1 -2 2
Find a basis for each eigenspace and calculate the geometric multiplicity of each eigenvalue. 3 2 The matrix A = 0 2 0 has eigenvalues X1 = 2 and X2 1 2 3 For each eigenvalue di, use the rank-nullity theorem to calculate the geometric multiplicity dim(Ex). Find the eigenvalues of A = 0 0 -1 0 0 geometric multiplicity of each eigenvalue. -7- Calculate the algebraic and
1. The symmetric matrix [4 1 1 1 A = 4-1 1 -1 4 -1 4 -1 has eigenvalues A = 1 (with algebraic multiplicity 1) and A 5 (with algebraic multiplicity 3). a) Find bases for the eigenspaces E(1) and E(5). b) Apply the Gram-Schmidt process to your basis for E(5) to find an onal basis for E (5) orthog- (c) Hence write down an that QT AQ = D. orthogonal matrix Q and a diagonal matrix D such...
Problem 6: (multiplicity) atrices given below, statethe einenvalus of the matieace, ox to do this one and give the algebraic and geometric multiplic ities of each. For each eigenvalue, give a basis for the eigenspace. OK to do this one ompletely in Octave, but be sure to interpret the answers it gives you (show tiny numbers like 1D-16 as zeros, and be sure to discard duplicate basis vectors) 4 0 0 0 0 0 4 0 0 0 A-2 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...
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...
Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval [0, 21). Round your answer to four decimal places, if necessary. If there is no solution, indicate "No Solution." V3tan(x) + 1 = 0 Answer How to enter your answer Keypad Keyboard Shortcuts Enter your answer in radians, as an exact answer when possible. Multiple solutions should be separated by commas. Selecting a radio button will replace the entered answer...
Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval [0, 21). Round your answer to four decimal places, if necessary. If there is no solution, indicate "No Solution." cot(-x) = -2cot(x) – 5 Answer How to enter your answer Keypad Keyboard Shortcuts Enter your answer in radians, as an exact answer when possible. Multiple solutions should be separated by commas. Selecting a radio button will replace the entered answer...
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