/*! 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} Q15E State true or false, if V聽bea l... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q15E (page 199)

State true or false, if Vbea linear transformation from Vto V,then the intersectionIm(T)andKer(T)must be {0}" width="9" height="19" role="math">

Short Answer

Expert verified

The given statement is False.

Step by step solution

01

Determine the linearity of T.

Consider a linear transformation T from V to V .

A function Tis linear transformation on D to DifT0=0.

A kernel of a function Tisdefined asKerT=fx鈭�P:Tfx=0.

02

Determine whether the statement is False.

By the definition of linear transformation and kernel of a function, the intersection of kerTand ImTis 0 means the intersection contain at least one element.

Hence, the statement is false

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

Question: TRUE OR FALSE?

4. The kernel of a linear transformation is a subspace of the domain.

TRUE OR FALSE?

7. State true or false, the spaceP1 is isomorphic to饾啅 .

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 P2given in Exercises 1through5 are subspaces ofP2(see Example 16)? Find a basis for those that are subspace,

{p(t):鈭�01p(t)dt=0}.

Show that if W is a subspace of an n-dimensional linear space V, then W is finite dimensional as well, and dim(W)鈮�n.

Question : Find the basis of al2脳2matrix S such that[1111]S=S, and determine its dimension.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

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.