/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q45E Question: If T is linear transfo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q45E (page 200)

Question: If T is linear transformation from V to V, then {f鈭�V:Tf=f} must be a subspace of V.

Short Answer

Expert verified

The solution is the statement is true.

Step by step solution

01

Define linear transformation

Consider that T is a linear transformation from V to V is defined by T(f).

There exist a linear transformation fromP6to C whose kernel is isomorphic toR2脳2.

Here, observe that T is mapping zero element to zero element which implies as follows.

T0=0

02

Determine if the statement is True or False

From the rank-nullity theorem as follows.

dimT=rankT+nullityTdimV=rankT+0dimV=lmT

As rank of T is dimension image space of T, which is always subspace of V

Therefore, the statement is true.

Thus, the given statement 鈥渋f T is a linear transformation form V to V then Tfis subspace of V鈥� is true.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Define an isomorphism fromP3 to R2脳2.

Let V be the space of all infinite sequences of real numbers. See Example 5. Which of the subsets of given in Exercises 12 through 15 are subspaces of V ? The arithmetic sequences [i.e., sequences of the form(a,a+k,a+2k,a+3k,...) , for some constants and K .

Show that if Tis a linear transformation from Vto W, thenT(0v)=0wwhererole="math" localid="1659425903549" 0vand0ware the neutral elements of Vand W, respectively. If T is an isomorphism, show that T-1(0w)=0v.

Find a basis of a linear space and thus determine its dimension. Examine whether a subset of a linear space is a subspace. Which of the subsets of given in Exercises 1through 5are subspaces ofP2 (see Example 16)? Find a basis for those that are subspaces,{p(t):p(0)=2}.

In Exercise 72through 74, letznbe the set of all polynomials of degree鈮�nsuch thatf(0)=0.

72. Show thatznis a subspace ofpnand find the dimension ofzn.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.