Question: Prove that the image of a span equals the span of the images. That is, where h: V W is linear, prove that if

Prove that the image of a span equals the span of the images. That is, where h: V → W is linear, prove that if S is a subset of V then h([S]) equals [h(S)]. This generalizes Lemma 2.1 since it shows that if U is any subspace of V then its image {h() | ∈ U} is a subspace of W, because the span of the set U is U.

Step by Step Solution

★★★★★

3.48 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

This is a simple calculation ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

961-M-L-A-L-S (5406).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Prove that a) b) c) d) e) L{1}(s) =-, s>0 Lie" }(s) =-a, , S a, a E R Cicos(b))>0, beR L{sin(bt))(s) s > 0, b E R s2+b2.

Let A be a nonsingular 2 Ã 2 matrix with singular value decomposition A = P QT and singular values Ï1 ¥ Ï2 > 0. (a) Prove that the image of the unit (Euclidean) circle under the...

(a) Prove that the polynomials i = 1.........k, are linearly independent if and only if the k (n + 1) matrix A whose entries are their coefficients aij ,1 i k, 0 j n. has rank k. (b) Formulate a...

3 Systems of differential equations Theorem 3. Any n linearly independent vectors in an n dimensional space V must also span V. That is to say, any n linearly independent vectors in an n dimensional...

Let t: V V be a linear transformation and suppose v V is such that tk(v) = 0 but tk-1(v) 0. Consider the t-string hv, t(v),....., tk-1(v)i. (a) Prove that t is a transformation on the span of the...

Show that for any subset S of a vector space, the span of the span equals the span [[S]] = [S]. (Members of [S] are linear combinations of members of S. Members of [[S]] are linear combinations of...

THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF MATHEMATICS AND STATISTICS JUNE 2015 MATH2501 Linear Algebra (1) TIME ALLOWED - THREE HOURS. (2) TOTAL NUMBER OF QUESTIONS - 5 (3) ANSWER ALL QUESTIONS (4)...

Please need help with no. 2. defined by T(v) = Av is a linear transformation from V to W. * 2 Prove that the image space of a linear transformation T from V to W is a subspace of W. 3 Let A be p x q...

According to the Stern Marketing Group, 9 out of 10 professional women say that financial planning is more important today than it was five years ago. Where do these women go for help in financial...

Determining Amounts to be Paid on invoices Determine the amount to be paid in full settiement of each of the Following invoices, assuming that credt for returne and allowances was received prior to...

Assume the bid rate of a foreign currency ( FC ) is USD 0 . 0 0 6 6 while the ask rate is USD 0 . 0 0 7 6 at Bank X . You observe at the same time at Bank Y , the bid rate of the FC is USD 0 . 0 0 7...

(Law of Diminishing Marginal Utility) Some restaurantsoffer all you can eat meals. How is this practice related to diminishing marginal utility? What restrictions must the restaurant impose on the...

In exercise 1 and 2, let A = PDP-1 and compute A4, 1. 2. 2 1 2 3

In Exercises 1 and 2, A, B, P, and D are n x n matrices. Mark each statement True or False. Justify each answer. 1. a. A is diagonalizable if A = PDP-l for some matrix D and some invertible matrix P....

A is a 5 x 5 matrix with two eigenvalues. One eigenspace is three-dimensional, and the other eigenspace is two-dimensional. Is A diagonalizable? Why?

Rust Bucket Motor Credit Corporation (RBMCC), a subsidiary of Rust Bucket Motor, offered some securities for sale to the public on March 28, 2008. Under the terms of the deal, RBMCC promised to repay...

1. The Global Business Travel Association reported the domestic airfare for business travel for the current year and the previous year. Below is a sample of 12 flights with their domestic airfares...

The next dividend payment by Wyatt, Inc., will be $3.00 per share. The dividends are anticipated to maintain a growth rate of 5.75 percent, forever. Assume the stock currently sells for $49.60 per...