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Homework Answers
Find the eigenspace corresponding to each eigenvalue of a. b. c. d. e. f. Find the...
Find the eigenspace corresponding to each eigenvalue
of
a.
b.
c.
d.
e.
f.
Find the eigenspace corresponding to each eigenvalue of A 3 8 (5) = 8A(-2) = 4 b. A- [12] {{ }) {{}) 841-2) = {{{ z?}) 841) = {{ --]) {[ -> ]}) 843) = {{{ 2 }) ( =>]}) 842) = 812) = {{{1}) 8A(7) = d. 8A(-5) = e. 8A(-1) = 8A(-3) = f. 8A(-1) = {}}}) 844) = {{{ ["}}
4. Let E) 6 3 0 [8 Marks] 3 6 0 A = 0 0 11...
4. Let E) 6 3 0 [8 Marks] 3 6 0 A = 0 0 11 a) Find the eigenvalues of A b) For each eigenvalue of A, find a basis for the corresponding eigenspace. c) Consider the linear transformation T : R3 -> R3 defined by T(x) = Ax for every xE R3. Find a basis of R3 in which the matrix representing T is diagonal
3 -1 0 Problem 11 Let A= 16 -5 0 0 16 0 -2 15 -3...
3 -1 0 Problem 11 Let A= 16 -5 0 0 16 0 -2 15 -3 -15 2 8 0 a) [3 pts) Compute the characteristic polynomial of A and find its roots. b) [4 pts) For each eigenvalue of A find a basis for the corresponding eigenspace. c) [3 pts] Determine if A is defective. Justify your answer. d) [6 pts) If A is defective, determine the defective eigenvalue or eigenvalues, and find a Jordan chain (or set of...
Problem 11 Let A= 3 -1 0 0 16 -5 0 0 16 0 -2 15...
Problem 11 Let A= 3 -1 0 0 16 -5 0 0 16 0 -2 15 -3 -15 2 8 a) [3 pts) Compute the characteristic polynomial of A and find its roots. b) (4 pts] For each eigenvalue of A find a basis for the corresponding eigenspace. c) [3 pts] Determine if A is defective. Justify your answer. d) [6 pts) If A is defective, determine the defective eigenvalue or eigenvalues, and find a Jordan chain (or set of...
hi, can you write the notation and everything? Assignment 12 Let A= -3 -5 -2 6...
hi, can you write the notation
and everything?
Assignment 12 Let A= -3 -5 -2 6 8 2 0 0 -2 [3pt] (a) Find the eigenvalues of A. (1pt] (b) Determine the algebraic multiplicity of each eigenvalue of A. [3pt] (c) Find a basis for each eigenspace for A. (1pt] (d) Determine the geometric multiplicity of each eigenvalue of A. [2pt] (e) Give a matrix P and a diagonal matrix D such that P-1AP = D.
Find the eigenspace corresponding to each eigenvalue of A A 13 4.2. O a. Ob. 8,15...
Find the eigenspace corresponding to each eigenvalue of A A 13 4.2. O a. Ob. 8,15 = ({}) 841-2) = ({{ }}) 821-1) = {[1]). 896-3) = {{ ?]) 847) = ({}]]). 8x(+2) = {{ {"}}) ({}]]). 8(a) = ({{ }}) 84(1) = {[ -]]). 8913) - ({{ :']) ={{{1}}) od 8A(-1) = O Of. 8A(-5) = 84(2) =
Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace...
Find the characteristic equation of A, the eigenvalues
of A, and a basis for the eigenspace corresponding to each
eigenvalue.
A = Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace corresponding to each eigenvalue. -7 16 0 1 1 005 (a) the characteristic equation of A 2+7 2–1 2–5 = 0 (1 - 5)(1 - 1)(x + 7) = 0 (b) the eigenvalues of A (Enter your answers from smallest to largest.)...
linear algebra Find the characteristic equation of A, the eigenvalues of A, and a basis for...
linear algebra
Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace corresponding to each eigenvalue. A= - -8 1 3 0 1 1 0 0 4 (a) the characteristic equation of A (b) the eigenvalues of A (Enter your answers from smallest to largest.) (11, 12, 13) = ( ]) (c) a basis for the eigenspace corresponding to each eigenvalue basis for the eigenspace of 11 basis for the eigenspace of 12 basis...
DETAILS LARLINALG8 7.R.004. Find the characteristic equation of A, the eigenvalues of A, and a basis...
DETAILS LARLINALG8 7.R.004. Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace corresponding to each eigenvalue. --8 1 2 011 005 (a) the characteristic equation of A A= (b) the eigenvalues of A (Enter your answers from smallest to largest.) (2, 22, 2₃) = (c) a basis for the eigenspace corresponding to each eigenvalue basis for the eigenspace of 1 = basis for the eigenspace of 12 basis for the eigenspace of 13...
2 (5 points) Recalled that null space of a matrix A € Mnxn is defined as...
2 (5 points) Recalled that null space of a matrix A € Mnxn is defined as N(A) = {r € R” : Ar =0}. Now, the eigenspace of A corresponding to the eigenvalue 1 (denoted by Ex(A)) is defined as the nullspace of A-XI, that is, EX(A) = N(A – XI) = {v ER”: (A – XI)v = 0}. You should have three distinct eigenvalues in Problem 1 above. Let say there are li, 12, and 13. (i) Find the...
Find the eigenspace corresponding to each eigenvalue
of
a.
b.
c.
d.
e.
f.
Find the eigenspace corresponding to each eigenvalue of A 3 8 (5) = 8A(-2) = 4 b. A- [12] {{ }) {{}) 841-2) = {{{ z?}) 841) = {{ --]) {[ -> ]}) 843) = {{{ 2 }) ( =>]}) 842) = 812) = {{{1}) 8A(7) = d. 8A(-5) = e. 8A(-1) = 8A(-3) = f. 8A(-1) = {}}}) 844) = {{{ ["}}
4. Let E) 6 3 0 [8 Marks] 3 6 0 A = 0 0 11 a) Find the eigenvalues of A b) For each eigenvalue of A, find a basis for the corresponding eigenspace. c) Consider the linear transformation T : R3 -> R3 defined by T(x) = Ax for every xE R3. Find a basis of R3 in which the matrix representing T is diagonal
3 -1 0 Problem 11 Let A= 16 -5 0 0 16 0 -2 15 -3 -15 2 8 0 a) [3 pts) Compute the characteristic polynomial of A and find its roots. b) [4 pts) For each eigenvalue of A find a basis for the corresponding eigenspace. c) [3 pts] Determine if A is defective. Justify your answer. d) [6 pts) If A is defective, determine the defective eigenvalue or eigenvalues, and find a Jordan chain (or set of...
Problem 11 Let A= 3 -1 0 0 16 -5 0 0 16 0 -2 15 -3 -15 2 8 a) [3 pts) Compute the characteristic polynomial of A and find its roots. b) (4 pts] For each eigenvalue of A find a basis for the corresponding eigenspace. c) [3 pts] Determine if A is defective. Justify your answer. d) [6 pts) If A is defective, determine the defective eigenvalue or eigenvalues, and find a Jordan chain (or set of...
hi, can you write the notation
and everything?
Assignment 12 Let A= -3 -5 -2 6 8 2 0 0 -2 [3pt] (a) Find the eigenvalues of A. (1pt] (b) Determine the algebraic multiplicity of each eigenvalue of A. [3pt] (c) Find a basis for each eigenspace for A. (1pt] (d) Determine the geometric multiplicity of each eigenvalue of A. [2pt] (e) Give a matrix P and a diagonal matrix D such that P-1AP = D.
Find the eigenspace corresponding to each eigenvalue of A A 13 4.2. O a. Ob. 8,15 = ({}) 841-2) = ({{ }}) 821-1) = {[1]). 896-3) = {{ ?]) 847) = ({}]]). 8x(+2) = {{ {"}}) ({}]]). 8(a) = ({{ }}) 84(1) = {[ -]]). 8913) - ({{ :']) ={{{1}}) od 8A(-1) = O Of. 8A(-5) = 84(2) =
Find the characteristic equation of A, the eigenvalues
of A, and a basis for the eigenspace corresponding to each
eigenvalue.
A = Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace corresponding to each eigenvalue. -7 16 0 1 1 005 (a) the characteristic equation of A 2+7 2–1 2–5 = 0 (1 - 5)(1 - 1)(x + 7) = 0 (b) the eigenvalues of A (Enter your answers from smallest to largest.)...
linear algebra
Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace corresponding to each eigenvalue. A= - -8 1 3 0 1 1 0 0 4 (a) the characteristic equation of A (b) the eigenvalues of A (Enter your answers from smallest to largest.) (11, 12, 13) = ( ]) (c) a basis for the eigenspace corresponding to each eigenvalue basis for the eigenspace of 11 basis for the eigenspace of 12 basis...
DETAILS LARLINALG8 7.R.004. Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace corresponding to each eigenvalue. --8 1 2 011 005 (a) the characteristic equation of A A= (b) the eigenvalues of A (Enter your answers from smallest to largest.) (2, 22, 2₃) = (c) a basis for the eigenspace corresponding to each eigenvalue basis for the eigenspace of 1 = basis for the eigenspace of 12 basis for the eigenspace of 13...
2 (5 points) Recalled that null space of a matrix A € Mnxn is defined as N(A) = {r € R” : Ar =0}. Now, the eigenspace of A corresponding to the eigenvalue 1 (denoted by Ex(A)) is defined as the nullspace of A-XI, that is, EX(A) = N(A – XI) = {v ER”: (A – XI)v = 0}. You should have three distinct eigenvalues in Problem 1 above. Let say there are li, 12, and 13. (i) Find the...
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