i have some algebra questions. please give me all the correct
answers. thank you
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i have some algebra questions. please give me all the correct
answers. thank you
Consider the...
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...
101-2019-3-b (1).pdf-Adobe Acrobat Reader DC Eile Edit iew Window Help Home Tools 101-2019-3-b (1...
101-2019-3-b (1).pdf-Adobe Acrobat Reader DC Eile Edit iew Window Help Home Tools 101-2019-3-b (1) Sign In x Problem 2 (Eigenvalues and Eigenvectors). (a) If R2 4 R2 be defined by f(x,y) (y, x), then find all the eigenvalues and eigenvectors of f Hint: Use the matrix representation (b) Let U be a vector subspace (U o, V) of a finite dimensional vector space V. Show that there exists a linear transformation V -> V such that U is not an...
I need some help on this problem. Thank you! 15. Consider the differential equation (*) х%3D Ах + vex where v is an eig...
I need some help on this problem.
Thank you!
15. Consider the differential equation (*) х%3D Ах + vex where v is an eigenvector of A with eigenvalue X. Suppose moreover, that A has linearly independent eigenvectors v', v2,... , v", with distinct eigenvalues Ар А, гespectively. (a) Show that (*) has no solution /(t) of the form V(t)= ae*. Hint: Write a= а у+.. +a, v. (b) Show that (*) has a solution /(t) of the form n 0)...
2. (5' each) Give short answers: (a) True or false: If Ai-Adi for some real number λ, then u is a...
linear algebra question
2. (5' each) Give short answers: (a) True or false: If Ai-Adi for some real number λ, then u is an eigenvector of matrix A. If a square matrix is diagonalizable, then it has n distinct real eigenvalues. Two vectors of the same dimension are linearly independent if and only if one is not a multiple of the other. If the span of a set of vectors is R", then that set is a basis of R...
solve them clear with details please thank you Q1. Let A = be a 2 x...
solve them clear with details please thank you
Q1. Let A = be a 2 x 2 matrix. 45 (a) Find the characteristic polynomial of the matrix A. (5 pts) (b) Find all eigenvalues and associated eigenvectors of the matrix A. (10 pts) (c) If A is an eigenvalue of A, what do you think it would be the eigenvalue of the matrix 5A?Justify your answer) (5 pts) 0 Q2. Consider the matrix A = 6 2 -5 0 -6...
subject: Linear Algebra if someone could answer and explain why the answers are correct that would...
subject: Linear Algebra
if someone could answer and explain why the answers
are correct that would be much appreciated. Thanks in
advance!!
Exercises 1. The set P2 of polynomials of degree less than or equal to two is a vector space under polyno- mial addition and scalar multiplication by real numbers. (a) (5 points) Show that the set A = {1, 2, 22) is a basis for P2. (b) (2 points) Find the coordinate vector of an arbitrary polynomial of...
Please do number 2 Assume all matricies are Mmxm(R) unless otherwise specified. 1. (1 point) Prove...
Please do number 2
Assume all matricies are Mmxm(R) unless otherwise specified. 1. (1 point) Prove or disprove that the eigenvalues of A and AT are the same. 2. (2 points) Let A be a matrix with m distinct, non-zero, eigenvalues. Prove that the eigenvectors of A are linearly independent and span R”. Note that this means in this case) that the eigenvectors are distinct and form a base of the space. 3. (1 point) Given that is an eigenvalue...
Please argument all your answers and explain why of your arguments so i can understand better and...
Please argument all your answers and explain why of your arguments so i can understand better and do not use advanced things im just taking linear algebra course. Let V be a vector space of finite dimension over a field K. T a linear operator over V and a eigenvector of T associated to the eigenvalue . If , show that . Being A any matrix associated to T in some basis of V. We were unable to transcribe this...
I need answers for question ( 7, 9, and 14 )? 294 Chapter 6. Eigenvalues and...
I need answers for question (
7, 9, and 14 )?
294 Chapter 6. Eigenvalues and Eigenvectors Elimination produces A = LU. The eigenvalues of U are on its diagonal: they are the . The cigenvalues of L are on its diagonal: they are all . The eigenvalues of A are not the same as (a) If you know that x is an eigenvector, the way to find 2 is to (b) If you know that is an eigenvalue, the...
Q3. Consider the vector space P, consisting of all polynomials of degree at most two together...
Q3. Consider the vector space P, consisting of all polynomials of degree at most two together with the zero polynomial. Let S = {p.(t), p2(t)} be a set of polynomials in P, where: pi(t) = -4 +5, po(t) = -3° - 34+5 (a) Determine whether the set S = {P1(t).pz(t)} is linearly independent in Py? Provide a clear justification for your solution. (8 pts) (b) Determine whether the set S = {p(t),p2(t)} spans the vector space P ? Provide a...
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...
101-2019-3-b (1).pdf-Adobe Acrobat Reader DC Eile Edit iew Window Help Home Tools 101-2019-3-b (1) Sign In x Problem 2 (Eigenvalues and Eigenvectors). (a) If R2 4 R2 be defined by f(x,y) (y, x), then find all the eigenvalues and eigenvectors of f Hint: Use the matrix representation (b) Let U be a vector subspace (U o, V) of a finite dimensional vector space V. Show that there exists a linear transformation V -> V such that U is not an...
I need some help on this problem.
Thank you!
15. Consider the differential equation (*) х%3D Ах + vex where v is an eigenvector of A with eigenvalue X. Suppose moreover, that A has linearly independent eigenvectors v', v2,... , v", with distinct eigenvalues Ар А, гespectively. (a) Show that (*) has no solution /(t) of the form V(t)= ae*. Hint: Write a= а у+.. +a, v. (b) Show that (*) has a solution /(t) of the form n 0)...
linear algebra question
2. (5' each) Give short answers: (a) True or false: If Ai-Adi for some real number λ, then u is an eigenvector of matrix A. If a square matrix is diagonalizable, then it has n distinct real eigenvalues. Two vectors of the same dimension are linearly independent if and only if one is not a multiple of the other. If the span of a set of vectors is R", then that set is a basis of R...
solve them clear with details please thank you
Q1. Let A = be a 2 x 2 matrix. 45 (a) Find the characteristic polynomial of the matrix A. (5 pts) (b) Find all eigenvalues and associated eigenvectors of the matrix A. (10 pts) (c) If A is an eigenvalue of A, what do you think it would be the eigenvalue of the matrix 5A?Justify your answer) (5 pts) 0 Q2. Consider the matrix A = 6 2 -5 0 -6...
subject: Linear Algebra
if someone could answer and explain why the answers
are correct that would be much appreciated. Thanks in
advance!!
Exercises 1. The set P2 of polynomials of degree less than or equal to two is a vector space under polyno- mial addition and scalar multiplication by real numbers. (a) (5 points) Show that the set A = {1, 2, 22) is a basis for P2. (b) (2 points) Find the coordinate vector of an arbitrary polynomial of...
Please do number 2
Assume all matricies are Mmxm(R) unless otherwise specified. 1. (1 point) Prove or disprove that the eigenvalues of A and AT are the same. 2. (2 points) Let A be a matrix with m distinct, non-zero, eigenvalues. Prove that the eigenvectors of A are linearly independent and span R”. Note that this means in this case) that the eigenvectors are distinct and form a base of the space. 3. (1 point) Given that is an eigenvalue...
I need answers for question (
7, 9, and 14 )?
294 Chapter 6. Eigenvalues and Eigenvectors Elimination produces A = LU. The eigenvalues of U are on its diagonal: they are the . The cigenvalues of L are on its diagonal: they are all . The eigenvalues of A are not the same as (a) If you know that x is an eigenvector, the way to find 2 is to (b) If you know that is an eigenvalue, the...
Q3. Consider the vector space P, consisting of all polynomials of degree at most two together with the zero polynomial. Let S = {p.(t), p2(t)} be a set of polynomials in P, where: pi(t) = -4 +5, po(t) = -3° - 34+5 (a) Determine whether the set S = {P1(t).pz(t)} is linearly independent in Py? Provide a clear justification for your solution. (8 pts) (b) Determine whether the set S = {p(t),p2(t)} spans the vector space P ? Provide a...
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