Show each of the 3 following matrices is symmetric and idempotent ( J is a matrix...

Question

Question

Show each of the 3 following matrices is symmetric and idempotent

( J is a matrix with all 1 s)

Answer 1

Answer #1

Ne knewmtrn A 2 1-1町 (I-H) H)

Answer 2

Similar Homework Help Questions

A matrix A is said to be idempotent if A2 - A. Show that each of...

A matrix A is said to be idempotent if A2 - A. Show that each of the following is idempotent. 1 nJ H-X(XX)- I-H I-J
6) In econometrics we frequently encounter matrices that are both symmetric and idempotent. Such a matrix A has the...

6) In econometrics we frequently encounter matrices that are both symmetric and idempotent. Such a matrix A has the properties A",4 and A#AA. Use these properties to show that OS a“ 1, where a" is the ith diagonal element of A. [7 points] 6) In econometrics we frequently encounter matrices that are both symmetric and idempotent. Such a matrix A has the properties A",4 and A#AA. Use these properties to show that OS a“ 1, where a" is the ith...
(1 point) A square matrix A is idempotent if A2 = A. Let V be the...

(1 point) A square matrix A is idempotent if A2 = A. Let V be the vector space of all 2 x 2 matrices with real entries. Let H be the set of all 2 x 2 idempotent matrices with real entries. Is H a subspace of the vector space V? 1. Does H contain the zero vector of V? choose 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two matrices in...

(f) Let A be symmetric square matrix of order n. Show that there exists an orthogonal matrix P su...

(f) Let A be symmetric square matrix of order n. Show that there exists an orthogonal matrix P such that PT AP is a diagonal matrix Hint : UseLO and Problem EK〗 (g) Let A be a square matrix and Rn × Rn → Rn is defined by: UCTION E AND MES FOR THE la(x, y) = хтАУ (i) Show that I is symmetric, ie, 14(x,y) = 1a(y, x), if a d Only if. A is symmetric (ii) Show that...
Q2) Please show all working out neatly. If the answer is neat and correct I will...

Q2) Please show all working out neatly. If the answer is neat and correct I will upvote. Thanks! :) 2. Prove (without using Theorem 2.5) that if A and B are symmetric matrices, A + B is idempotent and AB = BA = 0, then both A and B are idempotent. (Hint: Use Theorem 2.4. Then derive two relations between the diagonalisations of A and B.) Theorem 2.4 Let A1, A2, ..., Am be a collection of symmetric k x...
3. Let Y ~ N(aln, σ21n) and matrices B and A be such that BY and...

3. Let Y ~ N(aln, σ21n) and matrices B and A be such that BY and (n-1)s-YAY (a) Show that B = n-11, and A = 1-n-J where I is the identity matrix and J is the matrix of all ones (b) Show that A is idempotent. (c) Show that tr(A)- rank(A). ( d ) Compute AB .

1. For each of the following symmetric matrices, find an orthogonal matrix P and diagonal matrix...

1. For each of the following symmetric matrices, find an orthogonal matrix P and diagonal matrix D such that PTAP = D. 0 1 (а) А — 1 0 1 -1 1 0 2 -2 (Ъ) А %— -2 -2 -4 -2 2 |3 0 7 0 5 0 7 0 3 (с) А %— 1. For each of the following symmetric matrices, find an orthogonal matrix P and diagonal matrix D such that PTAP = D. 0 1 (а)...
Let A be an n x p matrix with n p. (a) Show that r(AA) = r(A). (b) Show that I - A(ATA) AT is idempotent. (c) Show that r(1-A(ATAYA") = n-r(A) Let A be an n x p matrix with n p. (a) Show tha...

Let A be an n x p matrix with n p. (a) Show that r(AA) = r(A). (b) Show that I - A(ATA) AT is idempotent. (c) Show that r(1-A(ATAYA") = n-r(A) Let A be an n x p matrix with n p. (a) Show that r(AA) = r(A). (b) Show that I - A(ATA) AT is idempotent. (c) Show that r(1-A(ATAYA") = n-r(A)
Help on Questions 1-3 Math 311 Orthogonal & Symmetric Matrix Proofs 1. Let the n x...

Help on Questions 1-3 Math 311 Orthogonal & Symmetric Matrix Proofs 1. Let the n x n matrices A and B be orthogonal. Prove that the sum A + B is orthogonal, or provide counterexample to show it isn't 2. Let the n x n matrix A be orthogonal. Prove A is invertible and the inverse A-1 is orthogonal, or provide a counterexample to show it isn't. 3. Suppose A is an n x n matrix. Prove that A +...

Exercise 1 Answer the following questions: a. Consider the multiple regression model y-Xe subject to a set of linear constraints of the form Cß-γ, where C is mx (k + 1) matrix. The Gauss-Markov condi...

Exercise 1 Answer the following questions: a. Consider the multiple regression model y-Xe subject to a set of linear constraints of the form Cß-γ, where C is mx (k + 1) matrix. The Gauss-Markov conditions hold and also ε ~ N(0, σ21) Is it true that we can test the hypothesis C9-γ using a k¿SSRfillm d SKreducedmodel Please explain b. Refer to question (a). Let H and Hi be the hat matrices of the full and reduced model respectively. Show...