![5. [2p] (a) In a two-dimensional linear space X we are given three bases e-(a, e f- (fi, f2), and g- (91,92). The change of b](http://img.homeworklib.com/images/323f375a-b138-42f9-98db-68b18573b64c.png?x-oss-process=image/resize,w_560)
ї) and the change of basis matrix from the basis g to the basis f is Find the change of basis matrix from the basis g to the basis e. 0-2 6-4 0 -1 18 8 6 -3 A) 2 8 0(C) 66 (D) 18 0
Homework Answers
Add Answer to:
5. [2p] (a) In a two-dimensional linear space X we are given three bases e-(a, e f- (fi, f2), and g- (91,92). The chang...
7. [2p] (a) In a two-dimensional linear space X vectors el, e2 formi a basis. In this basis a vector r E X has expansio...
7. [2p] (a) In a two-dimensional linear space X vectors el, e2 formi a basis. In this basis a vector r E X has expansion x = 2e1 + e2. Find expansion of the vector x in another basis 1 -2 er, e2, of X, if the change of basis matrix from the basis e to the basis e, s (b) In a two-dimensional linear space X vectors el, e2 forn a basis. In this basis a vector r E...
Let V be a vector space, and ffl, f2, fn) c V be linear functionals on V. Suppose we can find a vector vi e V such that fl (v) 6-0 but £2(v)-6(v) = . . .-m(v) = 0. Similarly, suppose that for all 1 i...
Let V be a vector space, and ffl, f2, fn) c V be linear functionals on V. Suppose we can find a vector vi e V such that fl (v) 6-0 but £2(v)-6(v) = . . .-m(v) = 0. Similarly, suppose that for all 1 i < n we can find vi є V such that fi(vi) 6-0 and fj (vi)-0 for alljöi. Prove that {fL-fa) is were linearly independent in V ly independent in V * . Prove also...
5. Let V-Pi(R), and, for p(x) E V, define f, f2 E V by 2 fi...
5. Let V-Pi(R), and, for p(x) E V, define f, f2 E V by 2 fi (p(x))p(t) dt and f2(p(xp(t) dt 0 0 Prove that (fi, f2) is a basis for V", and find a basis for V for which it is the dual basis
Suppose that V is a 3-dimensional vector space over a field F and T : V → V is a linear tion such that the corresponding F[x]-module structure on V is given by 7. V F[x]/(x3-x2-x + 1). Among the...
Suppose that V is a 3-dimensional vector space over a field F and T : V → V is a linear tion such that the corresponding F[x]-module structure on V is given by 7. V F[x]/(x3-x2-x + 1). Among the matrices A, B, and C given below, which are the matrix of T in some basis for V. Explain 1 1 0 0 0-1 B-10 1 A 0 1 0 0 1 1 0 0 -1 0 0 -1 (Note:...
QUESTION 5 Let V denote an arbitrary finite-dimensional vector space with dimension n E N Let B = {bi, bn} and B' = { bị, b, } denote two bases for V and let PB-B, be the transition matrix from B...
QUESTION 5 Let V denote an arbitrary finite-dimensional vector space with dimension n E N Let B = {bi, bn} and B' = { bị, b, } denote two bases for V and let PB-B, be the transition matrix from B to B' Prove that where 1 V → V is the identity transformation, i e 1(v) v for all v E V Note that I s a linear transformation 14]
QUESTION 5 Let V denote an arbitrary finite-dimensional vector...
Exercisel: Consider a physical system whose state space, which is three-dimensional is spanned by...
Exercisel: Consider a physical system whose state space, which is three-dimensional is spanned by the orthonormal basis formed by three kets lu, lu2) and lu). 1- In this basis, the Hamltonian operator H of the system and the observable A are written as H-h 1 0 0A where w is real constant. And the state of the system at tu0 is: 19(0)--lu:) + luz) + lus) 1- Calculate the commutator [H, A]. 2- Determine (H)s(Y(0)[H1Ψ(0) 3- Calculate ΔH,[H-hy-VIP-R2 = ((H2)-(HPF...
Font Styles Paragraph Definition 1: Given La linear transformation from a vector space V into itself,...
Font Styles Paragraph Definition 1: Given La linear transformation from a vector space V into itself, we say that is diagonalizable iff there exists a basis S relevant to which can be represented by a diagonal matrix D. Definition 2: If the matrix A represents the linear transformation L with respect to the basis S, then the eigenvalues of L are the eigenvalues of the matrix A. I Definition 3: If the matrix A represents the linear transformation L with...
1 point) Read 'Diagonalization Changing to a Basis of Eigenvectors' before attempting this problem. Suppose that V is a 5-dimensional vector space. Let S -(vi,... , vs) be some ordered basis...
1 point) Read 'Diagonalization Changing to a Basis of Eigenvectors' before attempting this problem. Suppose that V is a 5-dimensional vector space. Let S -(vi,... , vs) be some ordered basis of V, and let T-(wi.... . ws) be some other ordered basis of V. Let L: V → V be a linear transformation. Let M be the matrix of L in the basis Sand et N be the matrix of L in the basis T. Decide whether each of...
Linear algebra need to solve d,e,f,g,h You are given the following set of 5 vectors from...
Linear algebra
need to solve d,e,f,g,h
You are given the following set of 5 vectors from R4: 4. 7,s} = {<2,-3,4,-5),(1,-2,2,-3),(1, 2, 2, 1), (5,-3, 7,-6), (6, 7, 3, 7)}, S and 11,15, 1, 18) e R4. Form the augmented matrix a. Next, we will find the rref of the augmented matrix. Take turns going around the group in deciding what row operation to do next. All members of the group should do that operation. Check each other's work. Do...
Problem 3 (LrTrmations). (a) Give an example of a fuction R R such that: f(Ax)-Af(x), for...
Problem 3 (LrTrmations). (a) Give an example of a fuction R R such that: f(Ax)-Af(x), for all x € R2,AG R, but is not a linear transformation. (b) Show that a linear transformation VWfrom a one dimensional vector space V is com- pletely determined by a scalar A (e) Let V-UUbe a direet sum of the vector subspaces U and Ug and, U2 be two linear transformations. Show that V → W defined by f(m + u2)-f1(ul) + f2(u2) is...
7. [2p] (a) In a two-dimensional linear space X vectors el, e2 formi a basis. In this basis a vector r E X has expansion x = 2e1 + e2. Find expansion of the vector x in another basis 1 -2 er, e2, of X, if the change of basis matrix from the basis e to the basis e, s (b) In a two-dimensional linear space X vectors el, e2 forn a basis. In this basis a vector r E...
Let V be a vector space, and ffl, f2, fn) c V be linear functionals on V. Suppose we can find a vector vi e V such that fl (v) 6-0 but £2(v)-6(v) = . . .-m(v) = 0. Similarly, suppose that for all 1 i < n we can find vi є V such that fi(vi) 6-0 and fj (vi)-0 for alljöi. Prove that {fL-fa) is were linearly independent in V ly independent in V * . Prove also...
5. Let V-Pi(R), and, for p(x) E V, define f, f2 E V by 2 fi (p(x))p(t) dt and f2(p(xp(t) dt 0 0 Prove that (fi, f2) is a basis for V", and find a basis for V for which it is the dual basis
Suppose that V is a 3-dimensional vector space over a field F and T : V → V is a linear tion such that the corresponding F[x]-module structure on V is given by 7. V F[x]/(x3-x2-x + 1). Among the matrices A, B, and C given below, which are the matrix of T in some basis for V. Explain 1 1 0 0 0-1 B-10 1 A 0 1 0 0 1 1 0 0 -1 0 0 -1 (Note:...
QUESTION 5 Let V denote an arbitrary finite-dimensional vector space with dimension n E N Let B = {bi, bn} and B' = { bị, b, } denote two bases for V and let PB-B, be the transition matrix from B to B' Prove that where 1 V → V is the identity transformation, i e 1(v) v for all v E V Note that I s a linear transformation 14]
QUESTION 5 Let V denote an arbitrary finite-dimensional vector...
Exercisel: Consider a physical system whose state space, which is three-dimensional is spanned by the orthonormal basis formed by three kets lu, lu2) and lu). 1- In this basis, the Hamltonian operator H of the system and the observable A are written as H-h 1 0 0A where w is real constant. And the state of the system at tu0 is: 19(0)--lu:) + luz) + lus) 1- Calculate the commutator [H, A]. 2- Determine (H)s(Y(0)[H1Ψ(0) 3- Calculate ΔH,[H-hy-VIP-R2 = ((H2)-(HPF...
Font Styles Paragraph Definition 1: Given La linear transformation from a vector space V into itself, we say that is diagonalizable iff there exists a basis S relevant to which can be represented by a diagonal matrix D. Definition 2: If the matrix A represents the linear transformation L with respect to the basis S, then the eigenvalues of L are the eigenvalues of the matrix A. I Definition 3: If the matrix A represents the linear transformation L with...
1 point) Read 'Diagonalization Changing to a Basis of Eigenvectors' before attempting this problem. Suppose that V is a 5-dimensional vector space. Let S -(vi,... , vs) be some ordered basis of V, and let T-(wi.... . ws) be some other ordered basis of V. Let L: V → V be a linear transformation. Let M be the matrix of L in the basis Sand et N be the matrix of L in the basis T. Decide whether each of...
Linear algebra
need to solve d,e,f,g,h
You are given the following set of 5 vectors from R4: 4. 7,s} = {<2,-3,4,-5),(1,-2,2,-3),(1, 2, 2, 1), (5,-3, 7,-6), (6, 7, 3, 7)}, S and 11,15, 1, 18) e R4. Form the augmented matrix a. Next, we will find the rref of the augmented matrix. Take turns going around the group in deciding what row operation to do next. All members of the group should do that operation. Check each other's work. Do...
Problem 3 (LrTrmations). (a) Give an example of a fuction R R such that: f(Ax)-Af(x), for all x € R2,AG R, but is not a linear transformation. (b) Show that a linear transformation VWfrom a one dimensional vector space V is com- pletely determined by a scalar A (e) Let V-UUbe a direet sum of the vector subspaces U and Ug and, U2 be two linear transformations. Show that V → W defined by f(m + u2)-f1(ul) + f2(u2) is...
Most questions answered within 3 hours.
-
C++
Write a class Fraction that defines adding, subtracting,
multiplying, and dividing fractions by overloading standard...
asked 51 minutes ago -
This java code won't run and I can't figure out the problem with
it. Please help...
asked 1 hour ago -
Trace the following recursive methods:
a) isPal with the string “abccda”
b) isAnBn with the string...
asked 2 hours ago -
1. Which of the following is false about photosynthesis?
A. ATP is the molecule used to...
asked 3 hours ago -
A simple random sample of size n=64 is obtained from a
population with a mean of...
asked 4 hours ago -
(2 dimensions, 1 object, 2 accelerations)
1) A projectile is thrown with a wind. The wind...
asked 5 hours ago -
Brian makes $34,100 per year. How much can Brian expect to
contribute to FICA taxes in...
asked 6 hours ago -
To buy a new house you must borrow $155,000. To do this you take
out a...
asked 6 hours ago -
Spacely Sprockets is evaluating the construction of a new plant
on land the company purchased for...
asked 7 hours ago -
1. Consider a linear regression model of y on K regressors and
an intercept.
(i) Describe...
asked 7 hours ago -
Enter a balanced equation for the reaction between hydrochloric
acid and sodium sulfite.
Express your answer...
asked 7 hours ago -
Give a regular expression describing the language
{x | x ∈ Σ* and x does not...
asked 7 hours ago