Question: Suppose that T: U V and S: V W are linear transformations. Prove the following relationship between ranges. R(S T) R(S)

Suppose that T: U → V and S: V → W are linear transformations. Prove the following relationship between ranges.
R(S ο T) ⊆ R(S)

Step by Step Solution

★★★★★

3.42 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

This question asks us to establish that one set RS T is a subset of a... View full answer

blur-text-image
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)

Word file Icon

961-M-L-A-L-S (6105).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

(Appendix 12.A) A firm identifies the following relationship between the real wage it pays and the effort exerted by its workers. Real Wage Effort 8.............................. 7...

Q:

Suppose that f. V W is an isomorphism. Prove that the set {1, . . . , k} V is linearly dependent if and only if the set of images {f(1), . . . , f(k)} W is linearly dependent.

Q:

Suppose that U and V are isomorphic vector spaces. Prove that there are infinitely many isomorphisms between U and V.

Q:

Suppose that that T: U V and S: V W are linear transformations. Prove the following relationship between kernels. K(T) K(S T)

Q:

Suppose T: U V and S: V W are linear transformations and dim (U) = dim (V) = dim (W). Suppose that S T is invertible. Prove that S and T are individually invertible (this could be construed as a...

Q:

Homework. 1. Use the vectors u = (u1, ..., Un), V = (v1, ..., Un), and w = (W1, ..., Wn) to verify the following algebraic properties of R". ( a ) (utv) tw= u+ (v + w ) (b) c(utv) = cu + cv for each...

Q:

Please refer to the question below. Note: This is all that the question comes with! Question 1. a, lpt) Let V, W be vector spaces and T,S : V > W be linear transformations. Let 1:1, .. Hum E V. Prove...

Q:

QUESTION 1 V Select the mappings that are linear transformations Choose all that apply . 5 points Select the mappings that are linear transformations T : R - R such that T(x) = 21 T : R' -+ R such...

Q:

question 11 The producer of a weightloss pill advertises that people who use the pill lose, after one week, an average (mean) of 1.8 pounds with a standard deviation of 1.05 pounds. In a recent...

Q:

Q8. (10 points) Let A be an n x n matrix with eigenvalue and eigenvector Av = Av. We define A0 = I. Suppose that p is a polynomial. Prove that p()) is an eigenvalue of p(A). Q9. Let W be a subspace...

Q:

A three- sided die is tossed twice. The Verin diagram below reveals the information, where Ci, 2) means Ion the first toss and a on the second. ,2) (,3) (2,2) C2, 3) (3, 2) (3,3) where A is Hhe event...

Q:

Boeing Company has had its financial ups and downs. Recently, the CFO for Boeing helped turn its problems around by analyzing the amount of value each product was providing to the company's bottom...

Q:

41. Americas young people are heavy Internet users; 87% of Americans ages 12 to 17 are Internet users (The Cincinnati Enquirer, February 7, 2006). MySpace was voted the most popular Web site by 9% in...

Q:

6. The table below shows the production possibilities schedule for an economy. Production Alternatives Capital goods per period Consumer goods per period A 0 40 B 1 36 C 2 28 D 3 16 E 4 0 a. Putting...

Q:

Show that if v1......... vn span V {0}, then one can choose a subset vil,........vim that forms a basis of V. Thus, dim V = m n. Under what conditions is dim V = n?

Q:

(a) Prove that if v1,..., vm forms a basis for V Rn, then m

Q:

Let W V be a subspace. (a) Prove that dim W

Q:

8 QUESTION 1 1 points Bob has worked out that the following events are NOT independent in his sample group A - the person is over 50 B - the person prefers overseas holidays to local WA holidays...

Q:

Consider the following code: a[title] { font-size: 1em; } What part of the code above is considered the attribute? font-size a title None of the answers are correct.

Q:

Write a brief summary to clearly layout how much money the investor should invest in each stock in the optimal risk portfolio and what is the risk of the portfolio. Compare to individual stocks, what...