Problem 7: a) Show that the matrix A-I 5 we can use A to define an inner product onR2 by defining..erAir. b) With respect to this inner product, find an orthonormal basis for R2. c) With respect to t...

Question

Question

Problem 7: a) Show that the matrix A-I 5 we can use A to define an inner product onR2 by defining..erAir. b) With respect to

math Advanced-Math

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

A has c4-13 了 5-λ 81-41 g t V訶くg and 930 and - Schmid 9 we will Uae 4 4 oloemal ba 4 4- 了 4 4 4 - 24 AM d ll ㄒ了ヌ 03 ろ5 43 8 レ〉 2

Add a comment

Answer 2

Similar Homework Help Questions

Define an inner product on by setting Find an orthonormal basis for this space We were...

Define an inner product on by setting Find an orthonormal basis for this space We were unable to transcribe this image5SS | } = a by + 2(a,bz + agbg) - (4162 + azbi) - Carbs + ag02)
Question 3. Let 3 5/' and for x(2),y -(,) ER2 define (a) Show that the assignment (x, y) > (x,y) defined ın (1) us an nner product [10 marks (b) If a - (1,-1) and b - (1,1), then show that the...

Question 3. Let 3 5/' and for x(2),y -(,) ER2 define (a) Show that the assignment (x, y) > (x,y) defined ın (1) us an nner product [10 marks (b) If a - (1,-1) and b - (1,1), then show that the vectors a and b are lınearly ndependent but they are not orthogonal with respect to the inner product n (1) 3 marks] (c) Given the vectors a and b in (b), the set (a, by is hence a...
(i) Find an orthonormal basis {~u1, ~u2} for S (ii) Consider the function f : R3...

(i) Find an orthonormal basis {~u1, ~u2} for S (ii) Consider the function f : R3 -> R3 that to each vector ~v assigns the vector of S given by f(~v) = <~u1, ~v>~u1 + <~u2; ~v>~u2. Show that it is a linear function. (iii) What is the matrix of f in the standard basis of R3? (iv) What are the null space and the column space of the matrix that you computed in the previous point? Exercise 1. In...

for the subspace of R4 consisting of 4. Use the Gram-Schmidt process to find an orthonormal...

for the subspace of R4 consisting of 4. Use the Gram-Schmidt process to find an orthonormal basis all vectors of the form ſal a + b [b+c] 5. Use the Gram-Schmidt process to find an orthonormal basis of the column space of the matrix [1-1 1 67 2 -1 3 1 A=4 1 91 [3 2 8 5 6. (a) Use the Gram-Schmidt process to find an orthonormal basis S = (P1, P2, P3) for P2, the vector space of...
4. Consider the vector space V = R3 and the matrix 2 -1 -1 2 -1 -1 0 2 We can define an inner product on V by (v, w) =...

4. Consider the vector space V = R3 and the matrix 2 -1 -1 2 -1 -1 0 2 We can define an inner product on V by (v, w) = v'Mw. where vt indicates the transpose. Please note this is NOT the standard dot product. It is a inner product different (a) (5 points) Apply the Gram-Schmidt process to the basis E = {e1,e2, e3} (the standard basis) to find an orthogonal basis B. 4. Consider the vector space...
Exercise 5 Let z and y be linearly independent vectors in R" and let S- span(,y). We can use r and y to define a matrix A by setting (a) Show that A is symmetric (b) Show that N(A) S (c) Show tha...

Exercise 5 Let z and y be linearly independent vectors in R" and let S- span(,y). We can use r and y to define a matrix A by setting (a) Show that A is symmetric (b) Show that N(A) S (c) Show that the rank of A must be 2. Exercise 5 Let z and y be linearly independent vectors in R" and let S- span(,y). We can use r and y to define a matrix A by setting (a)...

Question B 7. (a) Let -1 0 0 (i) Find a unitary matrix U such that M-UDU where D is a diagonal matrix. 10 marks] (i)...

Question B 7. (a) Let -1 0 0 (i) Find a unitary matrix U such that M-UDU where D is a diagonal matrix. 10 marks] (i) Compute the Frobenius norm of M, i.e., where (A, B) = trace(B·A). [4 marks] 3 marks] (iii) What is NM-illp? (b) Let H be an n × n complex matrix (6) What does it mean to say that H is positive semidefinite. (il) Show that H is positive semidefinite and Hermitian if and only...
(1 point) Let {uj, u2, u2 ) be an orthonormal basis for an inner product space...

(1 point) Let {uj, u2, u2 ) be an orthonormal basis for an inner product space V. Suppose y = qui + buz + cuz is so that|lvl1 = V116. (v, uz) = 10, and (v. uz) = 4. Find the possible values for a, b, and c. a = CE (1 point) Suppose U1, U2, Uz is an orthogonal set of vectors in Rº. Let w be a vector in Span(v1, 02, 03) such that UjUi = 42, 02.02...
Find the matrix A' for T relative to the basis B'. T: R2 + R2, T(x,...

Find the matrix A' for T relative to the basis B'. T: R2 + R2, T(x, y) = (3x - y, 4x), B' = {(-2, 1), (-1, 1)} A' = Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R2, and let 0 2 A = 3 4 be the matrix for T: R2 + R2 relative to B. (a) Find the transition matrix P from B' to B. 6 4 P= 9 4...

Find the matrix A' for T relative to the basis B'. T: R2 R2, 7(x,y) -...

Find the matrix A' for T relative to the basis B'. T: R2 R2, 7(x,y) - (-9x + y, 9x - y), 8' = {(1, -1), (-1,5)} A' 11

Problem 7: a) Show that the matrix A-I 5 we can use A to define an inner product onR2 by defining..erAir. b) With respect to this inner product, find an orthonormal basis for R2. c) With respect to t...

Homework Answers

Add Answer to:
Problem 7: a) Show that the matrix A-I 5 we can use A to define an inner product onR2 by defining..erAir. b) With respect to this inner product, find an orthonormal basis for R2. c) With respect to t...

Post as a guest

Earn Coins

Define an inner product on by setting Find an orthonormal basis for this space We were...

Question 3. Let 3 5/' and for x(2),y -(,) ER2 define (a) Show that the assignment (x, y) > (x,y) defined ın (1) us an nner product [10 marks (b) If a - (1,-1) and b - (1,1), then show that the...

(i) Find an orthonormal basis {~u1, ~u2} for S (ii) Consider the function f : R3...

for the subspace of R4 consisting of 4. Use the Gram-Schmidt process to find an orthonormal...

4. Consider the vector space V = R3 and the matrix 2 -1 -1 2 -1 -1 0 2 We can define an inner product on V by (v, w) =...

Exercise 5 Let z and y be linearly independent vectors in R" and let S- span(,y). We can use r and y to define a matrix A by setting (a) Show that A is symmetric (b) Show that N(A) S (c) Show tha...

Question B 7. (a) Let -1 0 0 (i) Find a unitary matrix U such that M-UDU where D is a diagonal matrix. 10 marks] (i)...

(1 point) Let {uj, u2, u2 ) be an orthonormal basis for an inner product space...

Find the matrix A' for T relative to the basis B'. T: R2 + R2, T(x,...

Find the matrix A' for T relative to the basis B'. T: R2 R2, 7(x,y) -...

Problem 7: a) Show that the matrix A-I 5 we can use A to define an inner product onR2 by defining..erAir. b) With respect to this inner product, find an orthonormal basis for R2. c) With respect to t...

Homework Answers

Add Answer to: Problem 7: a) Show that the matrix A-I 5 we can use A to define an inner product onR2 by defining..erAir. b) With respect to this inner product, find an orthonormal basis for R2. c) With respect to t...

Post as a guest

Earn Coins

Add Answer to:
Problem 7: a) Show that the matrix A-I 5 we can use A to define an inner product onR2 by defining..erAir. b) With respect to this inner product, find an orthonormal basis for R2. c) With respect to t...