/*! 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} Q10E TRUE OR FALSE?10. If T is a line... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q10E (page 199)

TRUE OR FALSE?

10. If T is a linear transformation fromP6toR2脳2 , then the kernel of T must be three-dimensional.

Short Answer

Expert verified

The given statement is false.

Step by step solution

01

Definition of linear transformation

A linear transformation is a function from one vector space to another that respects the underlying (linear) structure of each vector space.

For example-

The defining characteristic of a linear transformation T:V鈫�Wis that, for any vectors v1andv2in V and scalars a and b of the underlying field,

Tav1+Tbv2=aTv1+btv2

02

Find the dimension of kernel of T

Dimension of p6is 7 and dimension of R2脳2is 4.

By rank theorem, 4=rankT*nullityT.

We can take zero transformation T that maps every vector to zero vector and its rank is 4,

So, the kernel of T is four dimensional.

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

Find the basis of all3脳3 upper triangular matrix, and determine its dimension.

Find the kernel and nullity of the transformation Tin(M)=M[1236]fromR2脳2toR2脳2.

Define an isomorphism fromP3 to R2脳2.

T denotes the space of infinity sequence of real numbers, T(f(t))=[f7f11]fromP2toR2.

Find out which of the transformations in Exercises 1 through 50 are linear. For those that are linear, determine whether they are isomorphism,T(x+iy)=y+ix
from to .
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Discrete 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.