Homework Answers
Add Answer to:
4. Let T be the linear operator on F which is represented in the standard ordered basis by the matrix c0 0 01 Let W be the nll space of T - c/. (a) Prove that W is the subspace spanned by 4 (b) F...
Problem 4. Give an example of a linear operator T on a finite-dimensional vector space such...
Problem 4. Give an example of a linear operator T on a
finite-dimensional vector space such that T is not nilpotent, but
zero is the only eigenvalue of T. Characterize all such
operators.
Problem 5. Let A be an n × n matrix whose characteristic
polynomial splits, γ be a
cycle of generalized eigenvectors corresponding to an
eigenvalue λ, and W be the subspace spanned
by γ. Define γ′ to be the ordered set obtained from γ by
reversing the...
Problem 4. Let V be the vector space of all infinitely differentiable functions f: [0, ]...
Problem 4. Let V be the vector space of all infinitely differentiable functions f: [0, ] -» R, equipped with the inner product f(t)g(t)d (f,g) = (a) Let UC V be the subspace spanned by B = (sinr, cos x, 1) (you may assume without proof that B is linearly independent, and hence a basis for U). Find the B-matrix [D]93 of the "derivative linear transformation" D : U -> U given by D(f) = f'. (b) Let WC V...
Two questions,please! 7. Assume C is a linear code. Prove that G is a generator matrix for C if and only if the columns of G form a basis of C 8. Let V. W U be vector spaces over F of finite dimen...
Two questions,please!
7. Assume C is a linear code. Prove that G is a generator matrix for C if and only if the columns of G form a basis of C 8. Let V. W U be vector spaces over F of finite dimension and φ: V → W, t : W → U linear maps. Prove that Im(φ)-ker( ) holds if and only if ψφ-0 and dimF1m(φ)-dimF kere).
7. Assume C is a linear code. Prove that G is...
4. Let T be a linear operator on the finite-dimensional space V with eharacteristie polynomial and minimal polynomial Let W be the null space of (T c) Elementary Canonical Forms Chap. 6 226 (a)...
4. Let T be a linear operator on the finite-dimensional space V with eharacteristie polynomial and minimal polynomial Let W be the null space of (T c) Elementary Canonical Forms Chap. 6 226 (a) Prove that W, is the set of all vector8 α in V such that (T-cd)"a-0 for some positive integer 'n (which may depend upon α). (b) Prove that the dimension of W, is di. (Hint: If T, is the operator induced on Wi by T, then...
Let T: Rr - be a linear operator such that ToT Id Show that there is a basis B &Trelative to the basis B {ui , , , , , щ, vı , . . . ,VJofR" such that the representing matrix T Ul,. .. ,ur, V...
Let T: Rr - be a linear operator such that ToT Id Show that there is a basis B &Trelative to the basis B {ui , , , , , щ, vı , . . . ,VJofR" such that the representing matrix T Ul,. .. ,ur, Vi, has the form wherer +s-n(r or smay be zero), ie., adiagonal matrix whose diagonal entries are all
Let T: Rr - be a linear operator such that ToT Id Show that there is...
Problem 3. Let V and W be vector spaces of dimensions n and m, respectively, and let T : V -> W be a linear transfor...
Problem 3. Let V and W be vector spaces of dimensions n and m, respectively, and let T : V -> W be a linear transformation. (a) Prove that for every pair of ordered bases B = exists a unique m x n matrix A such that [T(E)]c = A[r3 for all e V. The matrix A is called the (B,C)-matrix of T, written A = c[T]b. (b) For each n E N, let Pm be the vector space of...
6. Let T: P2P be the linear operator defined as T(p(x)) = P(5x), and let B...
6. Let T: P2P be the linear operator defined as T(p(x)) = P(5x), and let B = {1,x,x?} be the standard basis for P2 a.) (5 points) Find [T), the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x2 Determine [p(x)]s, then find T(p(x)) using [T]g from part a. c.) (1 point) Check your answer to part b by evaluating T(x + 6x) directly
Exercise 1. Let S(2) = (€1,6) be the standard basis of T R2 and let B...
Exercise 1. Let S(2) = (€1,6) be the standard basis of T R2 and let B = (? =-3e1 + 2e, v2 = 2e1-6). Show that B is a basis of T. Now suppose that a linear mapping f : T T is represented with respect to 8(2) by the matrix oSe 4 6' Find the matrix B that represents f with respect to B.
7.) 10points Let V be the space of 2 x 2 matrices. Let T: V-V be given by T(A) = A a.) Prove that T a linear transformation b.) Find a basis for the nullspace (Kernel) of T. c) Find a basis for the r...
7.) 10points Let V be the space of 2 x 2 matrices. Let T: V-V be given by T(A) = A a.) Prove that T a linear transformation b.) Find a basis for the nullspace (Kernel) of T. c) Find a basis for the range of T.
7.) 10points Let V be the space of 2 x 2 matrices. Let T: V-V be given by T(A) = A a.) Prove that T a linear transformation b.) Find a basis for...
Problem 3. Let V and W be vector spaces of dimensions n and m, respectively, and let T : V -> V be a linear transfor...
Problem 3. Let V and W be vector spaces of dimensions n and m, respectively, and let T : V -> V be a linear transformation (a) Prove that for every pair of ordered bases B = (Ti,...,T,) of V and C = (Wi, ..., Wm) of W, then exists a unique (B, C)-matrix of T, written A = c[T]g. (b) For each n e N, let Pn be the vector space of polynomials of degree at mostn in the...
Problem 4. Give an example of a linear operator T on a
finite-dimensional vector space such that T is not nilpotent, but
zero is the only eigenvalue of T. Characterize all such
operators.
Problem 5. Let A be an n × n matrix whose characteristic
polynomial splits, γ be a
cycle of generalized eigenvectors corresponding to an
eigenvalue λ, and W be the subspace spanned
by γ. Define γ′ to be the ordered set obtained from γ by
reversing the...
Problem 4. Let V be the vector space of all infinitely differentiable functions f: [0, ] -» R, equipped with the inner product f(t)g(t)d (f,g) = (a) Let UC V be the subspace spanned by B = (sinr, cos x, 1) (you may assume without proof that B is linearly independent, and hence a basis for U). Find the B-matrix [D]93 of the "derivative linear transformation" D : U -> U given by D(f) = f'. (b) Let WC V...
Two questions,please!
7. Assume C is a linear code. Prove that G is a generator matrix for C if and only if the columns of G form a basis of C 8. Let V. W U be vector spaces over F of finite dimension and φ: V → W, t : W → U linear maps. Prove that Im(φ)-ker( ) holds if and only if ψφ-0 and dimF1m(φ)-dimF kere).
7. Assume C is a linear code. Prove that G is...
4. Let T be a linear operator on the finite-dimensional space V with eharacteristie polynomial and minimal polynomial Let W be the null space of (T c) Elementary Canonical Forms Chap. 6 226 (a) Prove that W, is the set of all vector8 α in V such that (T-cd)"a-0 for some positive integer 'n (which may depend upon α). (b) Prove that the dimension of W, is di. (Hint: If T, is the operator induced on Wi by T, then...
Let T: Rr - be a linear operator such that ToT Id Show that there is a basis B &Trelative to the basis B {ui , , , , , щ, vı , . . . ,VJofR" such that the representing matrix T Ul,. .. ,ur, Vi, has the form wherer +s-n(r or smay be zero), ie., adiagonal matrix whose diagonal entries are all
Let T: Rr - be a linear operator such that ToT Id Show that there is...
Problem 3. Let V and W be vector spaces of dimensions n and m, respectively, and let T : V -> W be a linear transformation. (a) Prove that for every pair of ordered bases B = exists a unique m x n matrix A such that [T(E)]c = A[r3 for all e V. The matrix A is called the (B,C)-matrix of T, written A = c[T]b. (b) For each n E N, let Pm be the vector space of...
6. Let T: P2P be the linear operator defined as T(p(x)) = P(5x), and let B = {1,x,x?} be the standard basis for P2 a.) (5 points) Find [T), the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x2 Determine [p(x)]s, then find T(p(x)) using [T]g from part a. c.) (1 point) Check your answer to part b by evaluating T(x + 6x) directly
Exercise 1. Let S(2) = (€1,6) be the standard basis of T R2 and let B = (? =-3e1 + 2e, v2 = 2e1-6). Show that B is a basis of T. Now suppose that a linear mapping f : T T is represented with respect to 8(2) by the matrix oSe 4 6' Find the matrix B that represents f with respect to B.
7.) 10points Let V be the space of 2 x 2 matrices. Let T: V-V be given by T(A) = A a.) Prove that T a linear transformation b.) Find a basis for the nullspace (Kernel) of T. c) Find a basis for the range of T.
7.) 10points Let V be the space of 2 x 2 matrices. Let T: V-V be given by T(A) = A a.) Prove that T a linear transformation b.) Find a basis for...
Problem 3. Let V and W be vector spaces of dimensions n and m, respectively, and let T : V -> V be a linear transformation (a) Prove that for every pair of ordered bases B = (Ti,...,T,) of V and C = (Wi, ..., Wm) of W, then exists a unique (B, C)-matrix of T, written A = c[T]g. (b) For each n e N, let Pn be the vector space of polynomials of degree at mostn in the...
Most questions answered within 3 hours.
-
Write a program to solve the Josephus problem, with the following
modification:
Sample Input:
./a.out n...
asked 1 hour ago -
At the start of a CD it is spinning at a rate of 525 rpm
(revolutions...
asked 2 hours ago -
4. Without doing any calculations, predict whether the observed
∆T would increase, decrease or remain the...
asked 3 hours ago -
Based on the range, which of the following sets of scores has
the greatest variability? 3,...
asked 4 hours ago -
Ripples in a pond travel at a velocity of 3 m/s with one peak
passing a...
asked 4 hours ago -
A man stands on the roof of a building of height 13.0 mm and
throws a...
asked 4 hours ago -
The extent to which assets are financed by borrowed funds and
other liabilities is indicated by:...
asked 5 hours ago -
Explain in detail
Germany is the fifth largest economy
explain what goods and services Germany specializes...
asked 5 hours ago -
The density of platinum is 21.45 g/mL. If a cube of platinum
with a mass of...
asked 5 hours ago -
Accounts Receivable
Sales
A/R Posting
Extended Sales Invoice
Packing Slip
Compare invoice to packing slip 2...
asked 5 hours ago -
Michaella, age 23, is a full-time law student and is claimed by
her parents as a...
asked 5 hours ago -
Why are polymers not typically casted into products?
asked 6 hours ago