/*! 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} Q4E TRUE OR FALSE?聽4. The kernel of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q4E (page 199)

TRUE OR FALSE?

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

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

kernel of linear transformation

Kernel of linear transformation T is a set of all vectorsx such that T(x)=0.

So, it is a subset of the domain.

02

Explanation for the above statement

Let x, y are two vectors from kernel and a, b are two scalars, then for a linear transformation T we have.

Tax+by=aTx+bty=0+0鈬�0

So,ax+by is in kernel, meaning that the kernel of linear transformation is subspace.

Hence, the given statement 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

Find the basis of all 2脳2matrix A such that A commute with B=[1101],and determine its dimension.

In Exercises 5 through 40, find the matrix of the given linear transformation Twith respect to the given basis. If no basis is specified, use standard basis:渭=(1,t,t)forP2,

渭=([1000],[0100],[0010],[0001])

for鈩�2脳2and渭=(1,i)for,鈩�2脳2.For the spaceU2脳2of upper triangular2脳2matrices, use the basis

渭=([1000],[0100],[0001])

Unless another basis is given. In each case, determine whetherTis an isomorphism. IfTisn鈥檛 an isomorphism, find bases of the kernel and image ofTand thus determine the rank ofT.

17.T(z)=izfromCtoCwith respect to the basisB={1,i}.

Find the basis of each of the space V=Rm脳n, and determine its dimension.

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) = x from C to C

Find the image, kernel, rank, and nullity of the transformationT inT(f(t))=f(7) from P2to R.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

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.