7. Claim: Let A be an (n × n) (square) matrix. ·Claim: If A s invertible and AT = A-1 , then the columns of A form an orthonormal basis for R . Claim: If the columns of A form an orthogonal basis...

Question

Question

7. Claim: Let A be an (n × n) (square) matrix. ·Claim: If A s invertible and AT = A-1 , then the columns of A form an orthono

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

a 421 412 41 an A a1 2 I A 2 h 0 aAr Fim ⓥんe /u-ts..t 2 1 h- dif ete 12 A:t C4m // CG2.ノバ-. (ánn o01 d., 4 ↓。카 시.miu) 关.lt ta.blu, m rn torn on ort tier.onmo 1- baul^ ( 1p.n tan * oki Ca)- tI Thin AT.AT . IRA dxF As l buf-)4Λ @slumno 6 A.pw-

Add a comment

Answer 2

Similar Homework Help Questions

Prove the following: (a) Let V be a vector space of dimension 3 and let {v,U2,U3} be a basis for V. Show that u2, u2 -2+s and uvi also form a basis for V (b) Show that1-,1-2,1-- 2 is a basis for P2[r...

Prove the following: (a) Let V be a vector space of dimension 3 and let {v,U2,U3} be a basis for V. Show that u2, u2 -2+s and uvi also form a basis for V (b) Show that1-,1-2,1-- 2 is a basis for P2[r], the set of all degree 2 or less polynomial functions. (c) Show that if A is invertible, then det A (Note: Show it for any det A-1 square matrix, showing it for a 2 x 2 matrix...
2. Let B-[vi..... Vn] be an orthonormal basis of R". Prove that the matrix P (vilv2l...Vn) is ort...

2. Let B-[vi..... Vn] be an orthonormal basis of R". Prove that the matrix P (vilv2l...Vn) is orthogonal, that is PT P I, 2. Let B-[vi..... Vn] be an orthonormal basis of R". Prove that the matrix P (vilv2l...Vn) is orthogonal, that is PT P I,
please explain thoroughly :) Determine whether each of the following sets is orthogonal, orthonormal, or neither...

please explain thoroughly :) Determine whether each of the following sets is orthogonal, orthonormal, or neither A= 2- -J L2-1 Let U be an n × n matrix with orthonormal columns. Prove that det U-1.

please answer all the parts step by step 7 t o 17 1.1. Find orthonormal basis...

please answer all the parts step by step 7 t o 17 1.1. Find orthonormal basis of A= 0- 2 0 eigenrectors and eigenvalues, L1 0-1 1.2. Write A in the form A=U DU", where U is orthogonal matrix, Dis diagonal matrix 1.3. solve the problem u + Au=o, uco) = (1,0,00 1.4. Find orthonomal bases for R(A), R (AT), N(A), NIAT). 1.5. Is the system Ax=6, 6 = (1,1,17 consistent? 1.6. Find orthogonal projection of rector 6 outo |...
Let U be a square matrix with orthonormal columns. Which of the following is true of...

Let U be a square matrix with orthonormal columns. Which of the following is true of the columns of U? They are the same as the rows of U. The inner product of each pair of column vectors is 0. Each column vector has unit length. They are linearly independent B, C, D are correct. A, C, D are correct. All A, B, C, D are correct. Next Previous Let U be a square matrix with orthonormal columns. Which of...
(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...

(1 point) All vectors are in R". Check the true statements below: A. Not every orthogonal...

(1 point) All vectors are in R". Check the true statements below: A. Not every orthogonal set in R™ is a linearly independent set. B. If a set S= {ui,...,Up} has the property that uiU;=0 whenever i+j, then S is an orthonormal set. C. If the columns of an m x n matrix A are orthonormal, then the linear mapping 1 → Ax preserves lengths. D. The orthogonal projection of y onto v is the same as the orthogonal projection...
Let A be a diagonalizable n × n matrix and let P be an invertible n...

Let A be a diagonalizable n × n matrix and let P be an invertible n × n matrix such that B = P−1AP is the diagonal form of A. Prove that Ak = PBkP−1, where k is a positive integer. Use the result above to find the indicated power of A. A = −4 0 4 −3 −1 4 −6 0 6 , A5
A square matrix E∈Mn×n(R) is idempotent if E2=E. It is symmetric if E = tE. (a) Let V⊆Rn be a subspace of Rn, and consider the orthogonal projection projV:Rn→Rn onto V. Show that the representing matr...

A square matrix E∈Mn×n(R) is idempotent if E2=E. It is symmetric if E = tE. (a) Let V⊆Rn be a subspace of Rn, and consider the orthogonal projection projV:Rn→Rn onto V. Show that the representing matrix E = [projV]EE of proj V relative to the standard basis E of Rn is both idempotent and symmetric. (b) Let E∈Mn×n(R) be a matrix that is both idempotent and symmetric. Show that there is a subspace V⊆Rn such that E= [projV]EE. [Hint: What...

Let A be a diagonalizable n x n matrix and let P be an invertible n...

Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = p-1AP is the diagonal form of A. Prove that A* = Pokp-1, where k is a positive integer. Use the result above to find the indicated power of A. 10 18 A = -6 -11 18].46 A = 11

7. Claim: Let A be an (n × n) (square) matrix. ·Claim: If A s invertible and AT = A-1 , then the columns of A form an orthonormal basis for R . Claim: If the columns of A form an orthogonal basis...

Homework Answers

Add Answer to:
7. Claim: Let A be an (n × n) (square) matrix. ·Claim: If A s invertible and AT = A-1 , then the columns of A form an orthonormal basis for R . Claim: If the columns of A form an orthogonal basis...

Post as a guest

Earn Coins

Prove the following: (a) Let V be a vector space of dimension 3 and let {v,U2,U3} be a basis for V. Show that u2, u2 -2+s and uvi also form a basis for V (b) Show that1-,1-2,1-- 2 is a basis for P2[r...

2. Let B-[vi..... Vn] be an orthonormal basis of R". Prove that the matrix P (vilv2l...Vn) is ort...

please explain thoroughly :) Determine whether each of the following sets is orthogonal, orthonormal, or neither...

please answer all the parts step by step 7 t o 17 1.1. Find orthonormal basis...

Let U be a square matrix with orthonormal columns. Which of the following is true of...

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

(1 point) All vectors are in R". Check the true statements below: A. Not every orthogonal...

Let A be a diagonalizable n × n matrix and let P be an invertible n...

A square matrix E∈Mn×n(R) is idempotent if E2=E. It is symmetric if E = tE. (a) Let V⊆Rn be a subspace of Rn, and consider the orthogonal projection projV:Rn→Rn onto V. Show that the representing matr...

Let A be a diagonalizable n x n matrix and let P be an invertible n...

7. Claim: Let A be an (n × n) (square) matrix. ·Claim: If A s invertible and AT = A-1 , then the columns of A form an orthonormal basis for R . Claim: If the columns of A form an orthogonal basis...

Homework Answers

Add Answer to: 7. Claim: Let A be an (n × n) (square) matrix. ·Claim: If A s invertible and AT = A-1 , then the columns of A form an orthonormal basis for R . Claim: If the columns of A form an orthogonal basis...

Post as a guest

Earn Coins

Add Answer to:
7. Claim: Let A be an (n × n) (square) matrix. ·Claim: If A s invertible and AT = A-1 , then the columns of A form an orthonormal basis for R . Claim: If the columns of A form an orthogonal basis...